The other day a bizarre question popped into my mind: Is zero a number? On one level, the answer is obviously yes. Zero is not a letter, a flower, or a molecule. It is in the class of things we call numbers. While zero might be considered a number for classification purposes, does it truly exist in the real world? While I can point to three eggs and say, “Here are three eggs,” I cannot point to some X and say, “Here are zero Xs.” Zero does not correspond to anything in reality, because zero signifies the absence of reality. To say one has zero eggs is just a mathematical way of saying one does not have any eggs.
Of course, the same could be said of negative numbers like -1, -5, or -100. These numbers have no correlates in the real world. You will never find -5 apples. Negative numbers exist only in the mind. Of course, the same could be said of all numbers. While I can point to three eggs, five cows, or 17 cups, in none of these cases will I have located the numbers 3, 5, or 17. I will have only found instances in which a specific numerical value is exemplified by particular objects.
Perhaps to be considered a real number, a mathematical symbol must have an actual value. Since zero has no value, it is not a number. But why think having a value is necessary to be a real number? Is it special pleading to argue that the one numerical symbol that has no value is not a number simply in virtue of the fact that it alone has no value? Would we be unjustly excluding zero from the realm of numbers simply because it is unique among numbers? Perhaps.
What do you think? Is zero a number? Why or why not?
Thinking to Believe 
June 2, 2011 at 1:29 pm
I would say that zero is not only a number, but it does appear in the real world as well (as do negative numbers). Since I’m an electrical engineer, I’ll use an example from my field: suppose I am using a voltmeter to measure voltages between two points in a live circuit. Depending on the voltages at those two points and how I connect the voltmeter leads, the voltmeter may measure a negative number. Now, it is true that this negative voltage is just the voltmeter’s convention to report a negative number if the voltage at one of its leads is less than the voltage at the other. However, this negative number provides me with useful information in that it does tell me which voltmeter lead is connected to the higher voltage. If the voltmeter simply reported the absolute value of the voltage between its leads (i.e. positive numbers only) then I would have no way to determine which lead was connected to the higher voltage unless I already knew something about the circuit. Similarly, the voltmeter will report 0 volts if its two leads are connected to the same voltage — this is often a useful measurement to determine that the leads may be connected to parts of the circuit that are electrically connected together.
Also, your use of the term “real number” is interesting since the same term has a mathematical meaning that is different than the way you use it. Mathematically, a real number is a number such that its imaginary part is zero. The Wikipedia article on imaginary numbers (http://en.wikipedia.org/wiki/Imaginary_number) has some interesting things to say about this topic (take a look at the history and applications sections in particular).
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June 3, 2011 at 2:13 am
Null, surely though, the value zero doesn’t exist in the real world since your example doesn’t say 0 volts, it is interpreted that way since there is no voltage difference?
I believe it comes down to philosophy of whether an idea, however abstract can be defined as “real”. It certainly isn’t materialistic, and can therefore be used as a support of non-materialistic things. (My brother argued with an atheist basically proving God can exist if “3” exists – If you want further insight, I’ll chase it up?)
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June 3, 2011 at 3:41 pm
“When I use a word,” Humpty Dumpty said, in a rather a scornful tone, “it means just what I choose it to mean—neither more nor less.”
– Humpty-Dumpty talking to Alice in “Through the Looking Glass”
I opened my post with this quote, because this is exactly the attitude mathematicians take and you will see them calling numbers to many types of mathematical objects. If you look around, you will hear about all sorts of “numbers”: real, complex, cardinal, ordinal, p-adic, non-standard, surreal (I kid you not), etc. The terminology is not consistent nor particularly felicitous.
Zero is a mumber as good as any other. Think about it: if you have two numbers and you subtract them, you expect to get a number back right? So what is 1 – 1? This points out one reason why we declare zero is a number: if it were not, then a fairly innocent arithmetical operation like subtraction can produce a result that is not a number, which just complicates things with absolutely no gain whatsoever. And if nothing else, mathematicians are a very pragmatic bunch.
About the question, does the number zero exist? What is its ontological status? This is not really a mathematical question, but a question of the philosophy of mathematics. Some hold that they do exist, some do not, others that the question is meaningless — and I am probably oversimplifying as there are many philosophical schools on mathematics like constructivists of several persuasions, finitists, etc. I myself have no definite opinion on the subject, although I tend to favor a modest form of realism and lean to the yes-side of the fence.
I cannot make sense of your last paragraph. Numbers *are* values. A mathematical symbol should not be confused with what it denotes; if you want to be whimsical (or obfuscating) you could denote zero by the string of characters “I AM NOTHING AND PROUD OF IT”. It is absolutely irrelevant, because what the symbol denotes is a uniquely defined object, to wit, zero is the unique number that when added to itself is itself. In math lingo, 0 is the *unique* solution to the equation
x + x = x
The other numbers you know (1, 2, 3, etc.) can also be defined so that the symbols you used to denote them are really irrelevant.
Note: I am simplifying (or needlessly complicating…) things here. In some ways, this is not actually a very good definition but I hope I can get my message across.
Hope it helps, regards,
G. Rodrigues
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June 6, 2011 at 4:49 pm
Null,
I agree with you that negative numbers can be useful (indeed, accounting depends on them). But that’s a different question from whether or not negative numbers exist (you can owe me $5, but you will never find -$5 in the real world), or whether they should be categorized as numbers (even nominalists—who deny that numbers really exist—would fully agree that they are useful…fictions). The same is true of the number zero. It may be useful, but that does not mean it is a “real number.”
And no, I am not using that term as a technical term. I use it to refer to the ontology of numbers.
Jason
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June 6, 2011 at 4:49 pm
G. Rodrigues,
I like your point that if zero is not a number, then the answer to the equation “1-1=” would not be a number, which is absurd. But I did concede that zero is clearly a number in that sense. I am speaking about the ontology of zero (and with it, negative numbers). Does zero exist? And it seems you understand that this is the heart of my question. And you are right, it is a philosophical question.
By “values,” I am not referring to the symbol. I agree that we could choose any symbol to represent the value “1.” But there is a definite value we have in mind when we adopt a symbol to represent it. So what I was suggesting in my last paragraph is that perhaps for something to qualify as a number, it must have a value (regardless of the symbol we attach to it). Since zero has no value, it is not a number. But I think that this way of approaching the question might just be unjustly excluding zero by an ad hoc definition that favors excluding zero as a number.
I should disclose the fact that I lean toward the nominalist camp on this issue, so I don’t think any numbers truly exist. They are all useful fictions that help us make sense of reality. They are concepts only, having no extra-mental reality (I would not say–as the Platonists do–that numbers exist as abstract objects). But I ask the question about the existence of zero from a Platonist perspective. Since zero can never be instantiated in the real world, does zero exist?
Jason
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June 6, 2011 at 8:36 pm
Jason,
I did not say that negative numbers and zero are merely useful; rather, I said that they convey useful information. My position is that zero and negatives are numbers on equal standing with positive integers* (and all positive numbers, for that matter), since they all convey equally useful information. A measurement of -17V conveys different information than a measurement of 17V. In other words, if 1 is a number then so is 0 (I agree with G. Rodrigues, and his example that the result of 1 – 1 must be a number is excellent). Whether or not all numbers really exist or are merely useful fictions doesn’t particularly concern me (which is not to say that your post is uninteresting or pointless, but that the distinction is irrelevant to me as an engineer).
*All your examples are limited to integers. I wonder if you think numbers like 5.17 are “numbers” like the number 5 since in some contexts they do not exist in the real world. $5.17 is a “real” quantity (on paper, for example) but you cannot point to 5.17 dollar bills. What about $5.173? You cannot point to that even with dollars and pennies.
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June 7, 2011 at 11:35 am
Null,
What’s the difference between being useful and communicating useful information? Accounting that involves negative numbers provides us with useful information about what is owed to us, but the fact the remains that there are no “negative dollars” to be found in reality. It’s a useful concept that provides us with useful information, but that doesn’t mean it describes reality. Only positive realities exist. While the concept of negative numbers exists in our mind, actual negative numbers exist nowhere (unless you are a Platonist and think they exist in the abstract realm, but still, they don’t exist in the physical world).
I can see how our different areas of interest affect our answers here. As an engineer, you are thinking in very practical terms. I am thinking about metaphysics, and asking ontological questions.
I’m not sure I understand your *. I could agree that 5.17 dollars exist in a couple of ways. I could point to 5 whole dollar bills, and cut up another dollar bill into 100 pieces, and take 17 of those pieces and add it to the other 5. Or, since we use coins to represent partial dollars, I could represent that number using a combination of dollar bills and coins. In both cases I am able to point to positive realities that reflect the number in question. But the same cannot be said of zero or negative numbers.
Jason
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June 7, 2011 at 2:33 pm
Jason,
Something that is useful may not convey any information. A hammer exists in the real world and is useful, but does not convey any information. Zero and negative values convey information just as positive numbers (see my original voltage example), so I would say that they are numbers, too.
I understand that you are asking ontological questions. What I don’t understand is the value in the answer. I commented because (a) it seems obvious to me that 0 is a number, (b) I’m curious as to why you are asking this question (what value do you think you will derive from the answer?), and (c) it is an interesting thought experiment (though I find the answer to have zero 😉 value).
Regarding my footnote, my question is whether you consider certain values to be numbers (like the number 5) or not (like 0) if those values cannot exist in the real world in particular contexts. I gave dollar bills as an example of such a context. You can cut up a dollar bill into 100 pieces and place 17 of them next to five complete dollar bills, but are they really $5.17? No one would accept the 17 pieces as 17 cents — they are worthless so you really only have $5 (though you could say that you have 5.17 physical dollar bills). You could substitute pennies for the 17 pieces and get $5.17, but what about $5.173? You cannot possibly “point to” $5.173 in the real world because no combination of dollars and coins can equal this amount. Since you cannot “point to” $5.173 like you can point to 5 cows, is 5.173 a number in the context of money? I’m curious what your position is.
Also, you may find this interesting: http://books.google.com/books?id=63ooitcP2osC&pg=PA124#v=onepage&q&f=false\
Null
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June 8, 2011 at 4:04 pm
“So what I was suggesting in my last paragraph is that perhaps for something to qualify as a number, it must have a value (regardless of the symbol we attach to it). Since zero has no value, it is not a number. But I think that this way of approaching the question might just be unjustly excluding zero by an ad hoc definition that favors excluding zero as a number.”
That is my take on this, it is a purely ad-hoc definition.
“But I ask the question about the existence of zero from a Platonist perspective. Since zero can never be instantiated in the real world, does zero exist?”
You have repeatedly said that “zero has no value” or “cannot be instantiated in the real world”, but why would that constitute a valid criterion (for a platonist, that is) for determining the ontological status of a mathematical object? Surely what is true of 0 is true of the other numbers, and no one as far as I know has seen, smelled or touched the number 0 or the number 5 or for that matter, *any* and *every* mathematical object. At the moment I am typing, if I stop and look at my right hand I can see that it has 5 fingers, so the statement “My hand has 5 fingers” is true. Would you say that this is an “instantiation of the number 5”? Suppose I pick up a knife and chop off all of the five fingers in my right hand. Typing will be much harder but the sentence “My hand has 0 fingers” will be true. Why is that not an “instantiation” of the number 0?
I am not competent to discuss these (difficult) issues of the philosophy of mathematics (there is a book by M. Jubien on metaphysics that discusses some of these issues but I still have not had the time to go through it) but let me give another example. Let us take the infinite set constituted by all the natural numbers, that is, 0, 1, 2, etc. I will denote this set by N. Let me stress once again that this set is infinite, which for the purposes of my response just means not-finite. Is this set “instantiated” in the real world? What could this possibly mean? Well, one possible interpretation would be that the number of particles in the universe is not finite or the number of events since the beginning of the universe is not finite or some such similar statement. But according to the evidence we have, the number of particles in the universe *is* finite, the past *is* temporally finite and in fact, the universe having a not-finite number of “concrete thingies” (expression deliberately vague) entails all sorts of philosophical problems. According to your criteria, it would seem that N does not exist. But hold your horses. It is a standard exercise in a first course of quantum mechanics to study a (simplified) model of the hydrogen atom. What will the student find? That the set of energy levels that the electron can have *is* non-finite. Does this count as an “instantiation” of N? This is a common phenomenon in physics. To formulate these theories you have to lay hold of very abstract mathematical objects like manifolds, infinite-dimensional spaces, group representations, etc. Does the fact that the physical theories need these mathematical objects to formulate them automatically confers a positive ontological status on the objects themselves? If not, why not? And the reverse question too, I suppose.
Note for the cognoscenti: yes, the model is simplified and it is of a single hydrogen atom, hardly an accurate description of the universe. But for various reasons of a fundamental nature, the Hilbert spaces of quantum system are almost always infinite dimensional (e.g. the state space carries a representation of a symmetry group which for mathematical reasons *must* be infinite-dimensional) so the phenomenon is quite general.
Regards,
G. Rodrigues
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June 9, 2011 at 3:02 am
My previous post was already longer than it should have been or than I wanted to, but to quote Pascal (?), I did not have the time to write a shorter one. Nevertheless, I cannot resist and add that the nominalist (or formalist) answer always strikes me as a cop-out.
It is my impression that mathematicians secretly believe in the concrete reality of the objects they deal with, but when hard-pressed to justify that belief, unable or unwilling to do so, they retreat to the “it’s all a game” routine. The philosophical inability, while not an ideal state of affairs is understandable. With the increasing, but unavoidable specialization, it is all too easy to miss the forest for the trees. I certainly cannot give a justification for my realist belief. As for the unwillingness, if you are committed to an atheistic materialistic philosophy there is not much room for non-physical entities is there?
I stress that this is just an impression, or a psychological observation if you will, based on the tiniest of biased samples and anedoctal evidence, so feel free to dismiss it.
Regards,
G. Rodrigues
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June 9, 2011 at 5:12 pm
G. Rodrigues,
I only have a few minutes, so I’ll have to respond to your longer comment later, but I’ll say a few words about your shorter one now. First, I loved that quote. So true! It takes much longer to say less.
Secondly, I don’t think the issue of nominalism vs. realism (of whatever stripe) comes down to materialism vs. non-materialism. I am a theist, and yet I lean toward nominalism because of the arguments I have heard advanced against Platonism and for nominalism by the conservative Christian philosopher, William Lane Craig. By no means is this something I have studied much, nor have I come to any firm conclusions, but materialism is definitely not a factor. That said, nominalism is much at-home in a materialist worldview, so it would be a default position for a consistent and thoroughgoing materialist. It sort of reminds me of the evolution vs. design debate. If you are a materialist, then something like evolution has to be true. And yet even some theists believe evolution is the best account of biological diversity based on the arguments.
Jason
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June 14, 2011 at 4:05 pm
Doesn’t zero exist as a place holder? I was taught that it exists in this function. For example: 10, 20, 30, 40, 100, 1, 000, etc. Those are zeros, and they provide meaning for those numbers. In fact, those numbers couldn’t even be numbers without the zero present.
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June 14, 2011 at 4:56 pm
Aaron,
I think the distinction between a value and a symbol is important here. The symbol “0” is definitely part of those numbers, but it does not have the value of zero in those numbers (just like the “1” in “10” does not have the value “one” in “10”). So to be more technical, the question is whether the value zero exists.
Jason
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June 15, 2011 at 12:03 pm
G. Rodrigues,
You bring up some good points. Perhaps my difficulty with all of this is that I favor a nominalist view of numbers, and so on my view not only does zero lack any ontological status, but so does every other number. From a Platonist perspective, an abstract object does not have to be instantiated in the real world in order to be real, so even if zero was never instantiated in the real world, it still wouldn’t mean zero does not exist. It does, in the abstract realm.
There is no question that zero is meaningful. As your funny fingers analogy points out (no pun intended), when it comes to the question of how many fingers you have after chopping off 5 of them, there are zero fingers. But isn’t that just a way of saying when it comes to the question of value (which is what I understand the nature and function of numbers to be), no value can be assigned to the question of fingers? If you had only cut off four fingers, we could assign the value of 1 to the question of how many fingers you had. But if you cut off all five, the question of value ceases to be applicable because “nothing” has no value.
As for infinites, you are correct, I would say (with Cantor) that the infinite is nowhere to be found in reality. What about quantum mechanics? Well, when people who work in the field say that anyone who claims to understand quantum mechanics does not truly understand quantum mechanics, then I don’t feel too bad when I say I don’t understand quantum mechanics either. Granted my confession of ignorance, my initial response would be to say that this is just an example of useful fictions. Accountants need negative numbers to make accounting work, but that doesn’t mean that negative numbers can be instantiated in reality. Likewise, Stephen Hawking’s cosmological model required the use of imaginary numbers, but such numbers do not exist in reality. So while mathematical infinites may be useful in formulating models of quantum mechanics, I would not take that to mean that there must exist an infinite number of numbers, or that if an infinite number of numbers actually exists in the abstract realm, that the infinite set of numbers is actually instantiated in the real world. One of the features of abstract objects is that they are causally impotent, so even if numbers exist in a Platonic realm, and those numbers are actually infinite in number, they could not be causing anything in the quantum realm.
Of course, I will admit that perhaps I’m talking myself into confusion at this point! It’s been fun though.
Jason
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June 16, 2011 at 5:21 pm
To end my part this thread, let me just add a few clarifications.
1. It was not my intention to imply that nominalism vs. realism boils down to materialism vs. non-materialism. Theists have some wiggle-room; but if you are committed to an atheist-materialist view, nominalism is more or less a given. And since materialism is the default position in many circles…
2. I confess that I continue to be puzzled why on your nominalist view, you single out the zero as having no value. After all, zero much like any other number, is just a name for a concept. And as a concept it is just as good as any other.
3. The purpose of my examples on infinite sets and quantum mechanics was to try to understand your position better. I flatly deny that mathematical possibility entails ontological existence. A platonist may bridge the chasm by saying that there is no chasm, but if you are not a platonist you have work to do. This leads to my next point.
4. I am not a hard-core platonist, partly because of the argument you have put forth as well as others made by W. L. Craig, which while not conclusive are very reasonable. On the other hand, I have equal misgivings about nominalism. I would describe myself as a moderate realist, similarly to the Aristotelian-Thomistic middle-way position on the problem of universals. Unfortunately, I do not have the philosophical know-how to justify myself. This is a fascinating question but alas at the moment I have no time to pursue it. Maybe God will grant me the opportunity to find out more about it in the future.
By the way, congratulations on your blog. Your last post about traditional marriage is particularly insightful — pity the server with the link to the original paper is down.
Regards,
G. Rodrigues
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June 21, 2011 at 3:52 pm
In that case, I would say that the value zero does not exist. Zero and the word nothing are synonyms. Nothing doesn’t exist. Neither does zero. In fact, I would argue, that being equal to nothing, zero doesn’t even have a value. In order to have value or to have a value, it must be proven to exist. If zero, as a value, cannot be proven to exist, then it cannot be proven to have or be a value.
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June 22, 2011 at 7:35 am
This is a bit of a brain teaser…..
I think the actual question posed here is “does nothing exist” ?
I am not sure how to tackle this question, but can only say that in terms of the material reality, nothing is the state before God created the physical universe. As I say that I confuse myself more………..
Jason, where do you come up with this stuff ?? 🙂
Naz
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June 27, 2011 at 12:22 am
Thinking about ZERO reminds me of Jesus: From HERO to ZERO and than back again to HERO. In Philippians Chapter 2 it is described more detailled.
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July 21, 2011 at 12:56 pm
“0” must have existed because of your article!!! -> Note 0/0 “forme indeterminée”
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December 7, 2011 at 9:06 am
0 does not exist by definition let alone can be a number. Imagination gone wrong. It has no meaning in reality therefore is useless. It can have no specific physical location or represent any physical object. 0 causes lots of trouble in Maths and programming. If you are a programmer you will realise this. All the types of zero like null, 0, “”, [], {}, false, are the same thing i.e. non-existent, and just cause immense confusion, lost programming time and worst of all bugs. Zero and all its mirrors should be struck out of Maths and Programming. Don’t use symbols that have no meaning. Infinity is another one.
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December 13, 2011 at 9:18 am
It is an abstract construct of the human mind and language. It is a vehicle for moving a concept from the consciousness of one being to another, just like all numbers; and they also, do not exist. Written down they are just pen and ink ‘arrows’ which point to something ‘not’ them. Zero even points to its own absence!
I like an episode of Blackadder where one character is trying to explain counting to another.
“if we have one bean, and we add two more beans, how many beans do we have.”
“Some beans.”
“The renaissance just kind of passed you by didn’t it?”
There was a time when a billion did not exist, as it is a concept framed by Language, not an embodiement or truth. Without the mind to conceive it and perceive it, is irrelevant to the beans, they are just “some beans”.
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February 1, 2012 at 5:37 pm
yes 0 is a number. Without a 0 there would be no 10,20 30. Why would anyone want to discontinue the numerical process.
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May 29, 2012 at 12:46 pm
It is a number and the most important number of them all… If you look at the history of mathematics, positional number systems have beem possible only after zero was invented.
The concept of zero originated in India and the first decimal number system was also invented here.
Without zero, this entire number system would have never existed.
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May 29, 2012 at 1:27 pm
The utility of X does not mean X exists. Imaginary numbers are also useful in physics, but that does not mean they represent anything in the real world.
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November 5, 2012 at 11:26 pm
I was having a boring day, with only 1 subject at the last period. I typed an interesting question, and BOOOM! I found this site. I enjoyed reading all your comments and insights, (is even laughing). But I still stand as zero as zero. I don’t want to argue, so God bless everyone. 🙂
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January 26, 2013 at 8:36 pm
[…] the difference between zero people in a line segment and no people in an infinite line that’s so straight it wraps around […]
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April 3, 2013 at 9:50 am
Zero may be a “number” only in the same way “infinity” is a number–a tool that works in certain ways, with certain limits that don’t apply to “ordinary numbers” (including such “ordinary” numbers as imaginary and transcendental numbers).
In physics, we USED to think that a pure vacuum had “zero” density. Now the quantum people tell us about “vacuum pressure” and “virtual particles” and other kinds of counter-intuitive weirdness. It would seem that vacuum has “infinitesimal density,” not “zero density.”
Is it possible that the “zero” we take for granted is “really” an infinitesimal, not the absolute absence of quantity? To bring up quantum physics again, we no longer say that there is “zero chance” of a particular physical state, just a “very, very, very SMALL chance.” Thus the physicist David Deutsch speculates about the possibility of “Harry Potter universese” where people routinely play Quidditch–not because the laws of physics have changed, but because the VERY small chance of every atom simultaneously leaping UP instead of DOWN is a real number, not absolute zero.
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May 8, 2013 at 12:59 pm
….. some of this has been very interesting reading as well as highlighting quite a few people need a little more grounding with philosophical thought ….. by the way zero when written as 20 or 300 or 4000 is fulfilling the very same role as when it is 0 …. in ’20’ it tells us there are zero units ….. in ‘300’ it tells us there are zero units and zero tens …. you get the point.
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July 18, 2013 at 1:31 pm
[…] is what if. What if is grounded by probability. Probability is not necessarily definitive reality. Is Zero a Number? | Theo-sophical Ruminations Reply With […]
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September 2, 2013 at 8:57 am
Zero as “0” is nothing.
But its nothingness can stupendously
point to something.
e.g. 1/0, 3/0, 5/0 is equated to “infin”
or no end which is infinity. A thing
that math books would label as
undefined.
So, I regurgitate that Something divided by nothing as 0 = infinity aka spirit.
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September 21, 2013 at 7:02 am
No argument here zero is the number that makes it possible to measure less than 1, ie- 3 birds sitting on a fence , 1 flies away = 2birds sitting on a fence ,
1 flies away = 1 bird sitting on a fence so when it flies away how many birds , 0 of course. so the number of birds is now 0 that’s a number!!!!!!!!
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October 7, 2013 at 9:10 pm
Zero is a number. It just depends if you limit your idea of numbers to counting numbers only. Of course, you will probably not include 0 when you count, you start with 1.
In addition, when we talk of numbers, we talk about the same idea, thus numbers are representation of ideas we had in mind. If i say 0, you perhaps thinking of other idea, but if i say 0 eggs, then your will perhaps think of eggs as well. The point is, you have the same existing idea in both of you, which is the idea of “egg”. The existence of the “idea” matters, not on what we can “literally count as we see(or perceive) them.”
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October 29, 2013 at 3:53 pm
Interesting thought! I’m majoring in Philosophy and recently one of my classmates has been bringing up math a lot, and the only response my teacher can summon up is “Math is weird.”
I’ll have to show this to her.
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May 28, 2014 at 11:09 pm
No, I also thought the same. though, I couldn’t consider it a number for your reasons of “There’s zero of x’s” It only be in my opinion a class definition.
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June 10, 2014 at 6:30 am
….tnx for making me crazy at this point,,,,hmmmmmmm but i feel that math is very exciting….
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August 15, 2014 at 9:17 pm
I have zero comment and that will suffice.
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January 2, 2015 at 2:54 pm
We are conditioned to believe in zero being a number. We accept it because the “establishment” around us has drummed it into our mind.
But what if the general belief system did not accept that zero is a number?
Then if someone wrote 8 – 8 = 0, maybe the teacher would whack their knuckles with the ruler.
What if the following were written instead:
8 – 8 = “no value” – i.e. the statement is not valid.
It could be argued that the statement is no different from 8 / 0 = ?? (not valid).
Fact is, you can have a tenth of a penny or a hundredth of a penny and you still have “something”.. even a billionth of a penny. But the difference between any such “value” and zero is really undefinable. It’s similar to the concept of infinity in that regard.
I would be curious to see what would happen to the world of invention, design, and yes, math – if smart people started from this premise that zero is not a number and should not be used in equations.
Our way of thinking would be different. It’s not invalid!! It’s maybe more accurate than what we have now!
E.g. Okay I had a hundred dollars in your bank and I withdrew a hundred dollars.
Show me my bank statement please:
Your balance is: “Why do you have an account. Put money in please.”
Note at bottom of page:
“Oh and if you overdraw, we’re coming to your house to get something we can use to get our money back. In that case, we don’t send a bank statement, we send an invoice.”
If we all agreed that there’s no such thing as a negative balance, we’d have to rethink our world of calculating things. But if it were based on reality, instead of an imaginary concept, that wouldn’t be a bad thing, would it?
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September 20, 2015 at 9:36 pm
Zero is in fact a number, it is a real number as well as a rational number, 0 is the transition between negative and positive numbers. 0 is used to state the average eg.
1,2,3,4,5,6. Average (mean) would be 3.5, not 3 if we add 0, the average would become 3. (7 numbers instead of 6)
We do not state 0 in equations because in our language of maths we take out the beginning number if it is 0.
We do 1+2 not (0+1)+(0+2). There are multiple instances of the “number” zero, we use the same definition (0) for different things, let’s say:
The starting point of numbers is 0, we do not add this in equations, and the number 0 we can add to equations eg.
I will be using ¿ as the starting point and 0 as the number.
(¿+0)+(¿+2)+(¿+6)= 0+2+6= 8 or ¿+8
The mean:
Mean of(¿+0),(¿+2),(¿+6)= mean of 0,2,6 which would be 2.6•.
We can state 0 as a number but cannot state ¿ as a number even though ¿ we would call as 0.
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September 21, 2015 at 8:38 am
If you are holding zero (0) apples in your hand and I add one apple how many apples are you holding? One (1) Apple. Zero as a stand alone is nothing.
If you are holding zero (0) apples in your hand and you take away one apple, actually there are no apples to take away, so zero minus -1 or minus 0 to the nth power apples, you still have zero (0) apples.
Zero (0) is not a number by itself; zero is nothing ( ) zero only becomes or represents a number when it is used in conjunction with a real number. If you are holding nine (9) apples in your hand, besides having a really big hand, you would not be holding 9 plus 0 apples in your hand you would be holding 9 plus One (1) apple in your hand; AKA, Ten (10) apples because the zero represents one apple, not None apples. Zero apples here then represents one apple and not zero apples. It is not 9 plus zero apples ; the zero represents one plus the nine (9) you started with, expressed as ten or (10)
Now just in the hypothetical if you represented God The Father as zero (0), and God the Son as (0) and God the Holy Spirit as (0) what would you have? Zero plus Zero plus Zero = Zero; or, would you have zero plus One more zero plus One more zero? (0) plus (0) plus (0) = 3 zeros or One zero? You would have One zero because nothing plus nothing plush nothing equals nothing.
Now again in the hypothetical if you had one apple in your hand and you took 1 minus -1/2 ¿ (1 – 1/2 ¿) you would have not 1/2 apple but still one apple because (o minus 1/2 ¿) still equals zero a non number.
That is what it is like trying to define God in regular prose:
An agnostic is a wannabee believer sitting on the fence about what supernatural god myth to believe in, just in case. lol What part of ghost don’t you believe in? What part of Leprechaun don’t you believe in? Which Pasghetti Monster don’t you believe in?, if there was one:
What part of Darkness do you think might exist that prevents you from admitting it does not? In case I said that too fast; WHAT DOES DARKNESS CONSIST OF?
So we give nothing a name IN ORDER TO UNDERSTAND IT; and THEN, with a name and a convoluted set of other REAL things, it ENTERS reality? Kind of “sneaks” into our reality? I don’t think so.
You see, we are past masters at complicating the issue because “NOTHING” turns us on! So we hold onto nothing and describe it as reality.
NOTHING (0); AKA, SUPERNATURAL AND THE UNIVERSE AROSE
NOTHING (0); AKA, GOD AND THE UNIVERSE AROSE
NOTHING (0); AKA, BIG BANG AND THE UNIVERSE AROSE
NOTHING TURNS US ON !
OR
SOMETHING; AKA, THE UNIVERSE ALWAYS EXISTED AND IS THE CAUSE OF ITS OWN EFFECT.
UH UH. COMMON SENSE DOES NOT TURN US ON !
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December 14, 2015 at 5:35 am
I propose, like we have TEN WORDS to represent numbers, we should also have TEN NUMERALS to represent THOSE WORDS.
1,2,3,4,5,6,7,8,9,X
If we count with TEN-BASE math, it makes sense to give each of those numbers TEN CHARS as I wrote above.
So ini this case, 35+35=6X. As there are no zeros, what used to be Seventy (70) is now 6X. I think this also requires a rewrite of a lot of the words used to describe the hundreds, thousands, millions etc.
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December 16, 2015 at 7:29 am
Of course zero doesnt exists. Also plus and minus doesnt exist. 100% of math is pure insanity, denial of intelligent life and proof that people will blindly repeat anything. Our world is defined by transactions, relationships and tranformations. You can add and take. You cannot take what was not added. People will defend their intelligence and wisdom gained in school even though its pure crap. Its only intelligence and wisdom they have.
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December 16, 2015 at 10:31 am
I have an even BETTER idea. Let’s do away with “eleven” written as “11”. Let’s write it as “21”. This allows us to give a value of “HUNDRED” to the symbols “XX”. or “ten tens”. So 35+35=7X which we would normally write as “70 (seventy)”, but “79” in this new method we would think of as “69”. Confusing, but awesome.
So doing away with the “1” in the first digit space, allows us to more accurately and easily count the tens. You already had the “1” ten, with
1,2,3,4,5,6,7,8,9,X
Now your second ten is simply written with a “2” in front of it, to signify we are counting TWO tens.
21,22,23,24,25,26,27,27,29,2X – “two-X” means “20 twenty” in decimal. As you can see it still favors tens very well, but if the last digit is NOT ten “X” then we count down from 9 all the way to one, without chaning the “2”. So again, confusing at first, but i think is better.
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December 16, 2015 at 10:43 am
to clarify…
21,22,23,24,25,26,27,28,29,2X
equates to (when converted into traditional decimal)
11,12,13,14,15,16,17,18,19,20
got it?
Ok so 34+34 = 78. (68 the old way) But 35+35 = 7X (70 the old way)
You should understand better now!
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December 16, 2015 at 11:07 am
bah i was mixing old math with new math.
Ok so 34(24 old way) + 34 (24 again) = 58 (48 old way) 35(25 old way) + 35 (25 old way) = 5X(50 old way)
this is hard.
the chart:
1,2,3,4,5,6,7,8,9,X = 1,2,3,4,5,6,7,8,9,10
21,22,23,24,25,26,27,28,29,2X = 11,12,13,14,15,16,17,18,19,20
31,32,33,34,35,36,37,38,39,3X = 21,22,23,24,25,26,27,28,29,30
41,42,43,44,45,46,47,48,49,4X = 31,32,33,34,35,36,37,28,39,40
51,52,53,54,55,56,57,58,59,5X = 41,42,43,44,45,46,47,48,49,50
61,62,63,64,65,66,67,68,69,6X = 51,52,53,54,55,56,57,58,59,60
71,72,73,74,75,76,77,78,79,7X = 61,62,63,64,65,66,67,68,69,70
81,82,83,84,85,86,87,88,89,8X = 71,72,73,74,75,76,77,78,79,80
91,92,93,94,95,96,97,98,99,9X = 81,82,83,84,85,86,87,88,89,90
X1,X1,X3,X4,X5,X6,X7,X8,X9,XX = 91,92,93,94,95,96,97,98,99,100
Ok, so we see how we did the math using the chart. 35 + 35, remember we don’t count a “1” ever as a first digit, and as 35 correlates to 25 the old way of doing shitty math that you can see int he chart there, we don’t count one and then just count, 2, 3. So 3 + 3 in this new math system is a depending which spot the 3 is in. Remember to count in tens, we leave that one out, and just go to 21 instead 11. So if we start at 35, then that becomes our default ten, and is therefore a “1”, but you don’t have to think “1” just automatically go to 2, so 35+35 = 5X. Or 50 in the old way of shitty math.
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January 7, 2016 at 3:17 pm
Now it’s yours truly speaking for this HAPPY NE0 Year 2016 to all.
My new name is only J-0n!
And indeed i have made 0NE Resolution and not a ZER0 or 0 resolution!
Zero is a number and zero is also not a number. From the chain of dialogue in the past years everyone is correct, the are right always in accordance to their frame of reference. Everyone is a winner, it is always a win-win situation when we get together and ponder the reality of realities in all given subjects.
I’s astonishing and fascinating to deal with abstract and concrete terms of communication. So lets continue this year joyfully understanding the genesis of this question: Is zero a number?
Let me borrow some quotes from Lao Tzu to consider. He expressed,
“That by doing nothing, everything is done.” (Just wondering that nothing=0?)
Another guy in our time said, “That there are many poor people. The only thing the have is money.” ( I really wonder that by being poor is to have nothing=0?)
Finally, let me tossed my in the air my own definition of LIFE as
L=s/m 2
“Life is equal to spirit over matter squared”
(spiritual) (material)
When the value of m or material = 0 Q. What remains? A. s or spirit!
Reflect: L=s/0 = undefined or infinity (in religious parlance – eternity
So the reality of man in L.I.F.E.* is spirit (That is to say Spirit of Faith)
* LIFE has two or binary definitions: The Higher Definition and the Lower
LIFE = Living In Freedom Eternally / Living In Freedom Everyday
L = S / M
Additional equation i will tossed for this year is the existence of Triad Calendar
in this Day and Age that we live.
A.H. 1260 = A.D. 1844 = B.E. 1
It still has a zero number on it but it ended with 1 (as BE ONE)
Try to figure or do nothing (0)
B___________________________LIFE________________________e!
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January 24, 2016 at 3:47 pm
WE DESCRIBE AN EMPTY CONTAINER BY USING THE SYMBOL WE REFER TO AS 0. WE CAN EXPRESS IT “LEGALLY” AS A MATHEMATICAL STATEMENT AS 1(0) = 0. THE 1 STANDS FOR “ONE CONTAINER OR GROUP” AND THE SYMBOL 0 STANDS FOR “NOTHING” BEING IN IT. IN OTHER WORDS-ONE EMPTY CONTAINER WITH NOTHING IN IT IS EQUAL TO NOTHING. NUMBERS ARE SYMBOLS THAT WE USE TO COUNT ITEMS IN A CONTAINER. WE CAN NOT COUNT ANY ITEM BY USING THE SYMBOL ZERO. THUS ZERO CAN NOT BE USED TO DESCRIBE ANY AMOUNT. THUS ZERO CAN NOT BE CONSIDERED TO BE A NUMBER.
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March 13, 2016 at 8:33 am
I would say that because zero does not easily follow all the rules like other numbers that its status as a number is questionable. I think it’s much more like a concept similar to infinity. That doesn’t mean that it’s not useful as a concept and as a symbol (which are two distinct things). I really think there is something to this question.
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March 24, 2016 at 3:12 pm
There is no absence of reality. Therefore zero is not a number, but a concept.
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March 28, 2016 at 1:18 pm
I have discovered a better of counting with dozenal as well.
Again, just as we cannot use a zero unless you simply want that symbol to tell the observer that the object they are looking for isn’t there. We also cannot use a 1, as I’ve described earlier. So yes, we use 2 for the second digit spot.
But let’s understand better how to actually do the math by counting.
My theory is that 1 + 1 = 1. This is because it is easier to remember POSITIONS of numbers than taking the NEXT number past your starting number as position 1. So that means in traditional math, 1+1=2, but again, that is more confusing than 1+1=1. Because now we understand we are counting POSITIONAL LOGICAL NUMBERS. So now 2+1 = 2.
It’s kinda like 2×1, or 3,×1 so on. But we are adding not multiplying, but it’s different from actual addition i think we’d have to come up with another word to describe it.
2+TWELVE = 21
2 3 4 5 6 7 8 9 X [] /\ 1 – we start with 2, being a “1” position
1 2 3 4 5 6 7 8 9 X [] /\ – therefore “1” is it’s “TWELVE” position,
Ok to make this easier, we can also group the numbers into 3s, with 3 total groups.
123 – group 1 (FUNDAMENTAL GROUP)
456 – group 2 (SECONDARY GROUP)
7,8, 9,X, [],/\ – group 3 (MIRROR GROUP)
(1) (2) (3)
7 and 8 count as the first whole third of group 3 (1/3rd)
9,10 = second full third of group 3 (2/3rd)
11, 12 = third full third of group 3 (3/3rd)
In this case, to shortcut everything, we actually break everything down into it’s absolutely minimum fundamental. So we look at 1, well, it’s 1. But I actually think everything in the universe works on “threes”. So 1 is like a “fundamental 3”, so naturally if you have a “2” the fundamental of THAT is a “1”. And if you have a 3 the fundamental of course is a 2, and the reason for that is you have to have at least 2 to support a 3. You can’t just count 2 objects on a table and say you have 3, you have to have 2 and THEN add 1 to get 3!
Ok, so 1+1 = 1, 1+2=2, and so on. Those numbers are in the fundamental so whenever you add to fundamental numbers together, as long as it’s not 3+2, it’s sum is in group 1.
4+4 = 7, the reason for this is we are in the second group, therefore naturally in the case you use any 2 numbers from group 2, you must count your start group and another, to reflect the group being group 2 lol. 4 + 4 = 7 due to 4 being the “fundamental third” of group 2. therefore looking for 7,8 as a whole one third of your “group 3”. But you are adding another group 2 fundamental (4). So you have to fundamentally split 8 down to 7.
Get the pattern? It’s all about fundamentalizing all numbers used.
So 5 + 5 = 9. This is because, well we know both numbers we are “adding” together are the SECOND third of group 2. So what do we do? The rules are, we are in group 2 with both numbers, therefore we know we have to count up 2 positions group wise. So we are in group 3, and 5 is the second third so we look at the second third of group 3, that’s 10. But we add another 5, so that’s fundamental to 10, which is a 9!
It’s confusing at first but it’s better math.
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March 28, 2016 at 2:46 pm
Is Zero a number? The answer is a BIG FAT YES!
0 (zero; BrE: /ˈzɪərəʊ/ or AmE: /ˈziːroʊ/) is both a number and the numerical digit used to represent that number in numerals. It fulfills a central role in mathematics as the additive identity of the integers, real numbers, and many other algebraic structures.
So, in short, people often claim “zero is not a number” because they lack the background to understand the formal, rigorous definitions of the number system.
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March 29, 2016 at 8:26 am
@ spiritual giant
that’s because their definitions are retarded and we are replacing them with ones that are NOT.
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March 30, 2016 at 8:23 pm
I think zero is a number because it adds some value to lets say money. Example you give someone lets say a casual worker a written note to take it to the boss to give him 1000 and by mistake you write 100, will he or she be given the 1000 he asks or the written 100.
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March 30, 2016 at 11:56 pm
DOZENAL_LOVE
As the old adage says “who has the gold makes the rules”, it further indicates, “Who has the gold makes the definitions” and not just because someone claims the definitions are retarded.
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March 31, 2016 at 12:33 am
DOZENAL_LOVE:
It also seems to me that whether one accepts that zero is a number and another accepts that zero is not a number, in any case, regardless of what you call a rose it is still a flower by any name and therefore 0 remains the same whether it is called a number or not called a number. To debate the issue, in my opinion, is merely a niggler’s game and quite meaningless actually. A computer that recognizes 1’s and 0’s doesn’t matter if it is a number or not a number while the quantum computer recognizes information as 1 & 0 at the same time. It may serve as an intellectual parlor game for philosophical sleuths but that it serves any valuable purpose, I don’t think so.
It’s something like believers and non believers debating the definition of God or the existence of God…What is, is, regardless of debate. Roman Numerals were used up until the 15 and 16th centuries and is still used today but as to 0 The number zero does not have its own Roman numeral, but the word nulla (the Latin word meaning “none”) was used by medieval computists in lieu of 0. Bede or one of his colleagues used the letter N, the initial of nulla, in a table of epacts, all written in Roman numerals. according to Wiki’s references.
As it is we are stuck with the clock, hours in a day, months in a year, eggs in a carton.
Personally I think all planets are spherical which leaves Pluto in the game. Everything else are chunks of asteroids, meters and things that have never met their mesh. lol
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March 31, 2016 at 12:37 am
meteoroid
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April 2, 2016 at 8:53 am
@ Spirtual Giant
Computers don’t recognize “zeros”. Lol. “Zeros” in computer binary code is simply a “discharged transistor” which means the computer doesn’t read from it. It sits there and does nothing. The computer doesn’t read it, it’s not a value, it’s just “turned off”. So let’s count to three in binary.
01 = ONE
10 = TWO
11 = THREE
what you are doing is looking for the charged transistors. with binary code, that’s a “1”. This is a form of positional logic that counts by 2.
If i have 2 light bulbs with one dome around them to help mix their colors together, and I’m going to use 3 positions of 2 switches to get 3 different values for the colors that the light bulb will mix and shine through the dome.
then the “right” switch is “01” = Turns On Blue light bulb
the left switch is “10” = turns on red light bulb
and both switches turned on “11” = Turn on both light bulbs, and this makes the color “purple”.
So you see the zero in this case is not being “recognized” only the 1s contain values that you can see the effects of. The “zero” in this case only denotes that the opposite light bulb is not being “recognized” right now. But when i turn both switches on “11” THEN YES it is recognized as it being used to mess with the value.
So you see zero has absolutely no value, binary code is just “This is on” and the things that are not on aren’t being used! There is no “record” of a zero with computing. It’s probably confusing to you because you can “see” zeros in a binary code editor, but again the zeros aren’t being “read'” lol. When your CPU displays lines of code with “zeros” in them, it’s not “reading” them it’s just looking for a value among a block of transistors, and only shows a 1 when it detects them.
If for some reason your binary code editor/viewer wasn’t working right, you could say all the lines of code would be nothing but zeros, maybe something happened and you couldn’t detect the 1s so by default they just all showed up as zero. Again, it’s not reading zeros, with binary editors the computer does quite a bit more processing to show you lines of code where as with just pure binary code being executed on a CPU without LOGGING the data it processes, just does what the 1s tell it to do.
It’s the 1s in binary code that drive your computer to process things. Not zeros. We could say binary code is not really “binary”, you could say it’s “sinary” or singular-digit POSITIONAL logic.
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April 2, 2016 at 1:27 pm
Dozenal:
OIC…Oh well, I am not a student of math; I count faster by 10’s than by 12’s.
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April 4, 2016 at 12:15 pm
Rrrrtttt
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April 4, 2016 at 6:15 pm
[…] now and then I read about people who wonder whether zero is a number. It never occurred to me to question this, […]
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April 7, 2016 at 11:02 am
0 is not a number it’s a place holder. It has no value. 0 holds a place in 10 and other numbers alike to hold the ones spot and make a number larger
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April 7, 2016 at 12:29 pm
Arthur bethanis:
Your own comment seems to me, says that 0 HAS value…..
“…..to hold the ones spot and make a number larger”
If 0 makes the number larger, it must have value. Sounds like common sense to me.
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April 8, 2016 at 6:53 pm
As i often expressed everybody is right according to their frame of reference.
And if your reference is within the frame, it is boxed or canned. It is time to get out and see the whole process in the light of understanding. What we all need as the common denominator is UNITY. Unity of thoughts are challenges for it implies oneness like one unit or 1 However since 1 is just an illusion we come to see that there is nothing. Thus zero takes over and everyone dwells in idle fancy and vain imaginings, albeit unrealistic. So be it. Be!
B___________________________________________________________e!
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April 15, 2016 at 6:24 am
@ inquisitor
Zero is used to make other numbers larger yes, but it has no intrinsic value, it is a char to represent the end unit, but cannot do so without another number in front of it.
The problem with using zero at end units, is that it makes us think it’s the beginning of another unit of ten, but it’s not! We count in tens, the numbers should read after 99 … 9X (or any other SINGLE CHARACTER to represent ten) for one hundred, or “nine tens” but would be better if we used “XX” (ten tens) as one hundred, therefore “21” for “eleven”. Get rid of one it doesn’t make sense to use it at the beginning of a multiple-digit number.
Zero doesn’t have value, a zero is a zero and is merely a placeholder because they couldn’t figure out how to do what I just did.
XX should mean one hundred in 10-base counting.
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April 15, 2016 at 11:03 am
It doesn’t matter about intrinsic value; it has practical value.
It’s like your name; if you name is Thomas but everybody calls you Tom the that’s how they know you and to them Tom is your name and of you take that name to court it shall stand as a matter of practical law with the intrinsic name or not, it could just as well know you Henry The Dozenal or any other name, it is what they know you as and that has “evidentiary value” if not intrinsic value.
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April 15, 2016 at 1:50 pm
@ inquisitor
It does matter. What you are saying is that Zero has TWO meanings in math, one means “nothing of something, absolute ZERO” and the other is just a place holder for end-of-ten-base-unit.
So you have 2 different chars that happen to look the same but do something completely different.
Zero either means “nothing of” or is an actual value, but by itself, without other numbers in front of the “zero” char, it has no value, so you can’t say it has intrinsic value. It is a placeholder. It can’t be anything else.
We have the word “ten” to call “10”. We don’t call it “One Zero” we call it TEN. There is no reason why we can’t signify it as it’s own numeral, I propose “X”, as the romans used X to mean ten.
Counting with “zeros” at the end of each 10 base unit, doesn’t mean zero has a value, just because you say it does. It is a placeholder that works if you follow the rules, but it’s easier to just use one numeral, so with the first row
1,2,3,4,5,6,7,8,9,X
You have TEN individual chars.
In the second row.
1, 2, 3, 4, 5, 6, 7, 8, 9, X
===>>>> 11,12,13,14,15,16,17,18,19,1X <<<<===
You don't have to remember an extra number, normally we would write "20" for "twenty" (1X) at the end, forcing us to remember the next number in sequence before we can complete each row. In THIS case however we'd have to call it something different, but in each row it's easier to remember only 1 number as the first digit from right to left.
the char "zero" has no value, and that's what we have shown from the beginning of this post. Zero is one char, and it has no value as one char, by itself. That's all we've been saying the whole time. It's used as a "switch" but doesn't "add value" to a number. Ten is still NINE PLUS ONE MORE, regardless if you use 10 at the end or X to represent it. There is nothing mathematically necessary about the use of 0 in "ten" to mean "ten". It is an arbitrary way of end unit representation, deriving from our historically poor understanding of mathematical logic and rationality but also violent, murderous and napoleonic tyrannical control of the population that still persists this day, making you and countless others afraid to question it's logic.
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June 27, 2016 at 11:55 am
Okay, let me help you out here. Your question was, “is zero a number?” The answer will be given shortly.
What IS zero? Zero is a “whole number”, zero is a “rational number”, zero is a “real number”, zero is a “even number”, ect… If we define any of these (adjective) number’s to be a number, then zero is a “number” because it is all of those things, due to its properties.
The only reason i am not giving a definite “yes”, is because i have been searching for hours and there is no definition of “number” that doesn’t end up being circular, but i have learned that in mathematics, if something is a number, it must also be a value, and vice versa. So either zero is both a number and a value or it is neither, but that doesnt depend on truth as much as it does on WHAT IS THE DEFINITION OF A NUMBER?
Your question is meaningless because it is semantical, not logical, and that is not your fault, thats just the apparent and unfortunate truth here. Let me ask a more meaningful question. Does zero exist?
Here is how i define Existence: That which is (something).
Here is how I define Is: That which equals (something).
In order for something to exist, it must equal something, even if all that that is is itself. If something is not equal to itself it does not exist. For example, a round quadrangle does not exist. It is a concept, because all things are concepts, because a concept is a thing, and because a concept is that which can be thought of or discussed, there is no such thing as the absence of concept (as its own concept).
Zero is a concept, obviously. But does it exist? Does 0=0? The answer is yes. If 0≠0, then it would not exist. ∞ is an example of something that does not exist, because ∞≠∞. Infinity subtract itself is undefined (Ø), because infinity is greater then itself, because it is greater then all possible values. Transfinity exists, which is like a demi-infinity, because ω=ω, and the set of x numbers subtract itself equals zero.
I am not defining an existence as an reality, an existence can very well be mere imagination and theory, but a reality is something that exists independent of our perception of it. Zero would still exist even if any person was never born. Therefore zero is a concept, it exists, and it is real, as with any number (not defining ∞ as a number).
Zero is not the absence of value. Zero is the state of neutral value. No-Solution, Undefined, Indeterminate, or the symbol i use for those things “Ø” is the absence of value. Does Ø=Ø? The answer is Ø. It is the only phenomena that both equals and contradicts itself, because what both equals and contradicts itself? There is no solution to that question, for it is undeterminable and undefined. We conceptualize this as Ø! Ø is the absence of numbers, it is the empty set {}, and it is different from 0 because 1+0=1 but 1+Ø=Ø.
Ø does not exist!
But it is a concept, a symbol, and arguably a phenomena (of the mind at least)
Zero≠Nothing.
Zero is not nothing.
Nothing is “the absence of all things”. But (the concept of) “nothing” is a concept, so it is a thing, therefore nothing is the absence of itself, therefore IT MAKES NO SENSE. Nothing does not exist, and the concept of everything has the same problems.
Zero exists, nothing does not. Therefore they are different.
If you have 5 apples and you subtract 5 apples, you have 0 apples, not nothing. If you had nothing, you would lose your house, your car, your identity, your planet, EVERYTHING, yourself, and you would lose your ability to lose, and btw you would lose that too.
Zero also must exist due to the identity property. x+0=x. If zero did not exist, then it would be x+(DNE)=DNE, or x+Ø=Ø But 0 and Ø are two separate concepts, 0 is a part of the number line, Ø does not.
Zero is a number. Zero is a value. Zero exists. The absence of value is the absence of sense.
I hope this helped.
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June 28, 2016 at 3:55 pm
Cryptacritic:
It has helped…now it is clear as mud.
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July 7, 2016 at 2:00 pm
From the History of Mathematics there was a time when zero did not exist.
I think you can make a case that zero exists in the weak sense (can be established by postulates and primative notions to be non-contradictory) but does not exist in the strong sense. If you follow Bertrand Russell zero is one of his primative notions (from memory) If you consider zero the same as the first element in the Peano postulates then the first element could be 1/2 as he shows. Also there is a difficulty in confusing numbers with numerals. ‘Gamma’ III and 3 are numerals. Similarly with 0 and zero hence arguments from nothing do not relate to zero. Another case of too much eye contact in education and traihason of the Clerks. I think you have highlighted a real problem here. Infinity is too hard for me.
Cheers
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August 1, 2016 at 9:34 pm
0 isn’t a number, a number is an actual quantity that is represented by numerals (the Hindu-Arabic symbols) we use today that we call “numbers”. 0 is a place holder to indicate that there is nothing a number is 1 2 + because these symbols are saying that there IS something there a number of that something.
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August 2, 2016 at 12:12 am
Lumi:
Nobody cares if zero is a number or not a number; it doesn’t matter! The important thing is its function.
Of course everybody wants to make their little philosophical arguments and formulate some sort of reasoning that show they are academically adept but really what’s the point? It means NOTHING, not zero, your rationale.
Now maybe you think the way to deal with this is to engage in polite debate and to make all your little points and counter points and show us all what a clever dick you are and that would be great fun for you. And the good news is you don’t even have to worry about someone like me damaging your cause because you haven’t got a cause. What you’ve got is a hobby.
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August 20, 2016 at 4:10 pm
if it’s not a number then it has no function in math. Non-numbers cannot be used with number-dependent math! They don’t compute and are redundantly valueless!
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August 20, 2016 at 9:56 pm
It is what it is and that’s all that it is. A rose is still a flower by any other name.
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August 21, 2016 at 5:01 pm
@ leothegreater A rose maybe a flower, but what if you don’t have a rose or any other flower at all? You have nothing. Therefore you don’t have a flower. And zero is NOT a number
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August 21, 2016 at 8:25 pm
It doesn’t matter if zero is a number or not a number. It has a function and fulfills the function; therefore, it is a flower……who makes definitions? words
You’re stuck in the world of dozenal and you can’t seem to civilize into modernity. Let it go; it’s only a small point to niggle over and in reality it can mean whatever man wants it to mean.
Latin was a dominant language once and preferred because it was a dead language but it too has been relegated to the archival chest where all good viruses are destined.
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August 21, 2016 at 8:28 pm
Okay zero is not a number… Happy now?
What is it? Zero.
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August 24, 2016 at 7:35 am
@LeoTheGreater obviously we use zeros in counting numbers, but the idea was to get rid of that as it’s unnecessary. I’m not sure why you’re having such a hard time with this.
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August 24, 2016 at 7:38 am
@LeoTheGreater if you have no flower, then you don’t have a flower. You do not possess a flower if there is no flower….therefore it is NOT a flower because there is NO FLOWER THERE.
You liberals seem to think everything has no actual meaning and trying to attribute an absolute meaning to something is somehow “racist” and “non-progressive”. You liberals have become so mentally decrepit i wonder if you can even drive a vehicle to work.
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August 25, 2016 at 1:31 pm
DOZENAL_LOVE
Yes I drive a vehicle to work but it is a zero emission vehicle, that means the emission from my vehicle is “zero” nothing. lol
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August 25, 2016 at 2:45 pm
@LeoTheGreater mad yet? Zero emission of what? If you have nothing (No Thing), then it’s nothing. It’s a non-value. You can state that you are experiencing a non-number, non-value but it is only abstractly relative to the ABSENCE of an object, item or element in question. It’s still not a number.
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August 25, 2016 at 10:32 pm
The point is: it doesn’t matter if it is a number or not a number…who cares? And why would it even matter…it fulfills a function and that’s all there is to it….
Why do you have a problem about whether it is a number or not a number? It is a semantics niggling point and doesn’t contribute to anything constructive.. You only want it to conform to your notion of dozens….instead of tens….
Get over it; the world decides, not any member.
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August 25, 2016 at 10:45 pm
the world isn’t a living thinking being. An individual person is a living thinking being.
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October 2, 2016 at 4:23 pm
Zero is a number only if it is used with another number symbol.
If i give you $10,000 and take away all the zeroes you only have a $1.
Give me all the zeroes but only if there is a 1- 9 is in front of it.
I don’t want 0 dollars.
I am a simple man but that is my logic.
If you don’t think the zero is not a number then you only land up with an ammount front of it.
George.
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October 16, 2016 at 4:25 am
It’s not a number if infinity is not a number as it is it’s opposite as -1 is to 1.
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January 8, 2017 at 8:01 pm
“0” is a number as it is on the number line between 1 and -1, it is the only number that does not have an assigned positive or negative value. Some people argue that if infinity is not a number and only a concept, then 0 is not a number. 0 holds a place on the number line, infinity does not. This has been debated ad nauseam, and the consensus is that it is.
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February 4, 2017 at 6:52 am
Give me headphones
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February 4, 2017 at 7:45 am
I like it cup is very good
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March 29, 2017 at 1:23 am
@ ed warmoth it only has a place on the number line because you say it does. But saying something has intrinsic value to how we look at numbers doesn’t make it so. You have to prove it. I have proven the opposite. Zero has no value. It is useless and as i have already pointed out you do not need a zero to do math. Rather, give all ten numbers their own digit. So that means we just replace “10” for ten with another single digit symbol. That being X like the Romans perhaps, or whatever you desire.
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June 15, 2017 at 7:07 pm
I am just a lowley tooll maker I can not debate 0 with you guys I don’t think 0 is a no. buuuuuuuut if you put 0 on a value ie 10 with o zero on the end becomes 100 so in the simple world I does have value and so forth 1 million becomes 10 million yes it is a NUMBER
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September 21, 2017 at 8:13 pm
Zero is a number. Add zero to 100 and you now have 1000. Add dollars to the equation and you went from a meager 100 to a grand 1000.
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November 22, 2017 at 2:43 pm
I have seen so many posts and arguments for zero being a number. While the arguments are valid, zero is absolutely not a number.
My argument against zero being a number is the fact that you cannot devide by it. 1/0 is not infinity! It is the opposite of infinity! It is a black hole that swallows the universe. Dividing by zero is punishable by death.
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November 22, 2017 at 4:04 pm
Geoff:
I believe that whether 0 is number or not is for nigglers who cannot let it alone for want of waxing with their personal philosophical reasoning.
Maybe they think the way to deal with this is to engage it in polite debate and to make all their little points and counter points and show us all what clever dicks they are and that would be great fun for them. And the good news is they don’t even have to worry about someone like me damaging their cause because they haven’t got a cause. What they’ve got is a hobby.
Good cheers to ye all.
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November 6, 2018 at 8:26 am
Of course zero is an abstraction, as are negative numbers.
But, (until corrupted by recent definitions) zero was not a “natural” or “counting number”
Ask an olden times shepherd to count the sheep in a pen, and he (they were almost invariably male) would answer 1, 2, 3 etc etc.
For an empty pen he wouldn’t say “zero” but would look at you, puzzled, and answer “there aren’t any”. That is, he can’t count them because there are none to count.
As an abstraction, zero is a useful descriptor for “none”.
In mathematics, it’s a very useful (an essential even) number.
But it is different from the positive integers.
Lingusitically, it’s not so simple.
If a farmer has a few sheep he does not have zero.
If a farmer has fewer than 20 sheep, he has at least one.
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November 6, 2018 at 9:26 am
Is Eleventy six a number as much as Eleventy ten
If 9 + 1, both numbers, equal 10 how can ten be considered consisting of a number and a non number: 1 and a non-number? If you take away the non number because it is not a number then 9 + 1 = 1 because 1 is that which is and 0 that which is not.
By itself it is a non number for example sodium NA and chloride CL are themselves sodium and chloride but together they are salt. NACL therefore the non number remains a non number until it is hybred and as a hybrid becomes a number by fulfilling in a hybrid role. It takes on the role of two numbers 9 + 1 so that two numbers together united cannot possibly make a non number . So 1 and 0 is the salt that NA in union with CL makes and transforms, like metamorphosis.
Another analogy is the egg and the sperm. separately they are what is be together they metamorph to become a composite like salt.
To say that 0 is not a number by itself is correct but to say that 0 in union with a number is still not a number is nonsense for nigglers to niggle over in a game as meaningless as saying NACL is sodium and Chloride, it is not NACL are mere elemental denotation as one might research one;s ancestry but they are no longer one, together they are salt.
Is that clear as water + dirt? or, as clear as mud?
One could even niggle argue it this way because two is not a number, the reality is that only one is a number if I put a marble on the table I have one marble on the table, if I place another marble on the table then I do not have two marbles, I have 1 marble + 1 marble, separate, apart and unique; if I imagine them melding into one then the two ones become one two in case I said that too fast let me say it again, If I imagine the 1 marble melding with the other 1 marble then we could a call that as meaning 2 1’s becoming 1 2 because one two is equal to two ones.
Now if you had a bunch of marbles on the table and the table was on a small boat floating on a big lake and a big wind came against the small boat on the big lake and blew the marbles off the table into the water of the big lake would it be correct for me to say that you lost all your marbles?
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January 23, 2019 at 1:47 am
This site seems to have lost its marbles.
Just because you can’t count something in objects doesn’t mean that number doesn’t exist. Numbers exist as abstract concepts in the first place; it’d be more foolish to say that something like 1 or 2 sheep exists than saying that the actual numbers 1 and 2 exist (by the nature of 1 and 2 being abstract, 1 and 2 sheep are just approximate abstractions that describe the physical world, whereas 1 and 2 fulfil their entire own definition).
In actual fact, the vast majority of numbers can’t be counted in marbles or sheep. On the other hand, in order to count, one needs a number generator and an incremental operator. Think about electricity: ground (albeit vastly misunderstood as well) is seen as 0V, but it is generally the source of electrons for a circuit. In the same way, 0 as a number holds all the other numbers so you can form others by means of addition/subtraction (i.e. 0 – (-1) = 1).
That’s like saying straight lines don’t exist because nothing in this world can exactly make a straight line to infinitesimal resolution. SMH.
I challenge any philosophical neoliberalist hippie to describe any other number as being “more” or “less” real/defined than the number 0 if it so much doesn’t exist.
I furthermore challenge anyone to give me the difference in value of the defined number 1 over any given amount of time. If you can answer that while both keeping in mind that 1 is a “defined value”, 0 “is not a number”, and renaming concepts for the sake of renaming them just creates a semantical debate.
Lastly, for anyone saying that imaginary numbers aren’t “real” (in the sense of definition or real-life applications), you can drop off your phones by me. RF communication wouldn’t exist without them.
P.S. My apologies if I seem aggressive, it’s just that numbers are very dear to me and I have a very low tolerance for idiocy.
P.P.S. Please realize that Mathematics is a branch that gives rise to its own existence. Just by defining Mathematics as a consistent system, its internal definitions make sense. It only describes our universe–it never equated to it. Trying to define Mathematical concepts in the scope of constrained scenarios is like trying to judge a human’s personality by his ability to breathe. There’s more to it than apples and sheep, people…
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January 23, 2019 at 10:06 am
Zero is not a number for the simple reason that you cannot divide anything by zero. The result is the opposite of infinity. It is a black hole that swallows the universe. In some institutions, dividing by zero is punishable by death.
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January 23, 2019 at 10:13 am
GEOFF:
Your definition is hideous just like the penalty of countries that would impose death for such things and other things like blasphemy. This is from a people who don’t know anything and will kill you to prove.
I prefer “…btirbaoqlis’s…” submission as practical and more soundly reasoned and you can reject it if you want but you won’t get a capital punishment sentence for so doing.
Have no part or association with anything for which a capital punishment is a sentence. Run as fast as you can because you can’t run faster than that.
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January 23, 2019 at 10:21 pm
@Geoff: Comments like these tend to remind me that pigeons are good chess players. I think you win, sir.
@LTG: You cannot sensibly reject 0 being a number. It’s like saying that the word “good” is not an adjective. It’s like saying lungs are not organs. It’s like saying the sky is not blue. Sure, you could live your life convinced that the lies you’ve been led to believe are true… but it makes no sense to do so.
Don’t get me started on the arguments with shifting the 0-9 to 1-X system. If you don’t see the problem in this approach, you don’t understand 0, numerical symbols, numbers, Mathematics, or anything else.
If you don’t understand that 0 is meant exactly what it’s meant to be, then you should probably also rather just stay quiet. 0 is a number because the number set needed a friend that’d allow them to be idempotent in an additive mathematical statement. Zero is needed numerically for the notion of physical quantities remaining the same: something that is unintuitive because of the laws of Thermodynamics, but nonetheless important. If anything, it is a number before it’s a value.
And no, it’s not that dividing by zero will implode the universe. It just hints at another quantity in Mathematics (infinity) that has to exist for a damn lot of our Mathematics to make sense (look up on infinity, limits, calculus). It hints at a part of Mathematics that works up to this point, but it’d be more logical to say that eventually infinity will be counted as a number than 0 as a non-number.
I’ve laid my case. Believe what you will–but don’t try be “philosophical” and “anti-mainstream” and “different” for the sake of forsaking a sound mind. Remember, there are people out there that believe it’s okay to murder people just because their special snowflake convictions dictate so. You don’t want to be that guy…
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January 24, 2019 at 1:32 am
Thanks BTIRBAOQLIS. Glad you agree with me.
Was that bear in your gravatar smoking a cigar that popped out of its mouth when it yelled Kiai?
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January 24, 2019 at 12:02 pm
The question here is, ‘Is zero a number?’
I’m not suggesting that zero isn’t a concept or even that it isn’t necessary, it is.
A number, however, it is not. Is infinity a number? Same argument. Zero has more in common with infinity than it does with numbers.
YOU CANNOT DIVIDE BY ZERO
That’s all there is to it.
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January 24, 2019 at 12:11 pm
Geoff:
Wouldn’t 1 divided by 3 have the same affinity to infinity. So I clicked up my computer calculator and divided 1 X 0 and I was surprised at what came up on my calculator which nothing but numbers has ever come up before with anything but numbers including zeros but this time what came up surprised me it was a text answer that said: “NOT A NUMBER” and I have a Mac so how can Apple be wrong about that.
Hey that’s one for the record books. 🙂 🙂
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January 24, 2019 at 11:11 pm
Dear @Geoff:
You are thinking of numbers without thinking of operators, or otherwise algebraic structures that give sense to the numbers.
Infinity is not defined as a number because there are no operators (save for limits, which relinquishes the definition of numbers) that can take us there. You can’t add, subtract, multiply, divide, take the exponent or power (or anything else) any numbers in order to yield infinity.
However, there are an infinite amount of ways to yield zero from mathematical operations: you can subtract a number from itself, you can multiply any number by zero, you can add any finite amount of zeros, or by definition, e^(i*pi) + 1.
That’s why infinity is a number and zero is not: because of the way that the algebra we use was set up. Looking at number theory and abstract algebra, there are many ways that mathematical algebras can be set up, but the reason the one we use is agreed upon, is because it so closely describes what we know: the universe as we know it.
It might be tempting to say that zero isn’t necessary or even more ludicrously, that zero doesn’t exist. But it’s the same as saying that atoms don’t exist because there was a time that people didn’t know about them or factored them in when it came to describing the universe. The fact of the matter is, the question cannot be answered–but to our closest approximation, if you mean “existing” to be the being of something that we perceive as humans, the concept and definition of zero, along with its arbitrary properties, do certainly exist as much as anything else that we “know”.
Lastly, just to clarify: zero is really dissimilar to infinity–I don’t get why people seem to think they’re similar for some reason. Anything divided by zero does not equate to infinity, either way (that’s where limits come again; under a limit, there are several ways of defining numbers divided by zero, and sometimes the limit value of some expression may equate to infinity–this branch of Mathematics is called calculus). I think more focus should be put into the fact that trying to divide by zero would yield a result that’s not classified as an element of the set that we’re allowed to work with. So there are three options of going ahead: (1) accepting that dividing by zero doesn’t yield a number, and that certain workarounds in the form of approximations may still yield interesting results (as mathematicians are currently doing), (2) to update how we view Mathematics in order to incorporate these paradoxical concepts (try to imagine a new colour), or (3) foolishly stating that zero is not a number simply because the above two options require an understanding of Mathematics not available to you, maybe by capacity, or maybe by lack of wanting to reason by logic as we know it.
It should be worth noting that if and only if someone came out with a new system of Mathematics as described in point (2), which would invalidate zero as being a number for some reason, only then would it be viable for debate that zero might not be a number.
Fun fact: The value zero is closely associated to a concept in Mathematics known as triviality. For example, when trying to find x for some polynomial without a constant coefficient, the trivial solution for that polynomial will be x = 0. Similar concepts apply in linear algebra, and other fields of Mathematics. It’s ironic that zero should be associated so closely to triviality, when in fact it’s downright trivial (and nonsensical) to say that the number zero “does not exist”.
TL;DR: Would you argue with me that green isn’t a colour, simply because the concept of green (even though supported by Mathematics and the physical universe) was defined by someone? No? Maybe it’s time to change your mind about zero not being a number. Otherwise, happy chess playing, all y’all pigenos.
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January 26, 2019 at 1:48 pm
Dear btirbaoqlis,
I am very familiar with operations and have had more instruction in math than I would ever care to list. This debate is really rather ludicrous.
So we can divide any infinite amount of numbers by any infinite amount of numbers and yield any infinite amount of numbers. Except when the denominator is zero. Lol how can zero be considered a number?
Look at it another way. The opposite of numbers could be described as the absence of numbers. That’s zero!! Not a number but the absence of a number.
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January 26, 2019 at 4:46 pm
How about this?
Zero (disambiguation) can satisfy everybody:
Zero is both the digit 0 and the number 0.
0 (zero) is both a number and the numerical digit used to represent that number in numerals. The number 0 fulfills a central role in mathematics as the additive identity of the integers, real numbers, and many other algebraic structures. As a digit, 0 is used as a placeholder in place value systems.
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January 20, 2020 at 6:49 am
Zero is not a number. It is a symbol for nothing. It is a necessary symbol which has no value. Because you can not show me zero of anything, it represents nothing. Nothing is not divisible by 2, because you cannot divid eby nothing, it doesn’t exist. Otherwise all things would be divisible by nothing to create confusion. If numbers were divisible by zero, so then could be elephants or clowns. Two clowns divided by zero = zero clowns. So, you started with nothing and ended up with nothing. But is it twice as much nothing? No. There can not be twice as much of nothing.
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October 8, 2022 at 11:47 am
Can we say rotten eggs as negatively countable?
All we have is an interpretation becs number we refer is just quantify things but negative and positive terms qualify the objects.Like we edible eggs or apples can be positively countable and non-edible eggs or apples can be negatively countable.
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November 10, 2022 at 3:16 am
I thought it’s not a number but i realize that if there’s no zero then there’s no 10 20 30…
right?
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May 25, 2023 at 2:03 pm
…finite creatures duking it out with all our finite strength to understand that which is impossible to figure out (i.e. infinity)… Which is more important: Love or Knowledge?
The bible says God is “one”, “three”, “infinite”. That’s why faith is the mechanism he gives us to understand him in our hearts. There is much to learn and much to know about the more important things in life: belief, heaven, hell, where you are going when you die. Interesting question about 0, but let’s not pretend 0 and infinite are simply mathematical concepts. They do also deal largely with the spiritual realm: the mind, the spirit, the unknown…
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July 16, 2023 at 11:17 am
Your explanation is not giving sense. You are saying 0 is not a number and again you are also saying is a number. Say one thing please
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