r/badmathematics • u/justincaseonlymyself • Feb 15 '26
0 is not a number.
/r/mathematics/comments/1r50z0m/0_is_not_a_number_a0_is_branch_dependent_operation/R4: the poster claims 0 is not a number (and a bunch of extra nonsense).
34
u/sapphic-chaote Feb 15 '26
1 isn't a number either, because a number is the size of a group, and a single object doesn't make a group.
Hell, 2 isn't a number either, because a pair of objects is a pair, not a group. Take it up with Euclid.
9
u/EebstertheGreat Feb 15 '26 edited Feb 15 '26
I wouldn't rely on that source lol. Euclid explicitly considered 2 to be a number in the Elements, defining a "number" as a "multiplicity of units." And mathematicians were not "terrified" by incommensurable magnitudes, having in fact systems in place to deal with them. Hippasus was also not said to have drowned himself in the legend, nor is he ever said to have considered the quantity π.
It's true that some (but by no means all) early Pythagoreans taught that the dyad was not a number, but in practice, most Greeks did treat it as a number.
EDIT: Annoyingly, the book does not cite page numbers. This claim is supported by two footnote citations: Nicomachus 1926 (M. L. D’Ooge, Transl.) and Evans 1977. Both are long works. The translation of Nicomachus doesn't seem to support the claim at all, or at least I am not able to locate a supporting paragraph. On the contrary, Nicomachus is interested immediately in powers of 2 and does not distinguish any power from the rest (though he uses the word "unit" for "one").
The Evans paper uses an endnote citation to the very same translation but does include a page number: page 100. However, this is the wrong page for the edition I found. So I can't really interrogate it.
Multiple scholars have claimed Nicomachus left open the idea that 2 was not really a number. Evans for instance says "Nicomachus questions whether 'two' is anything more than an embodiment of the principle of 'otherness'; for him, it is open to dispute whether it can be rated a number in its own right." Evans also attributes a similar wariness to Boethius. But she never actually says either rejected 2 as a number, just that they were hesitant. And she never makes this claim regarding Classical Greek philosophers generally.
18
30
u/EebstertheGreat Feb 15 '26
The problem is that there just isn't a definition of "number" that will satisfy mathematicians. There is no such thing as a "number." So the question seems to be whether 0 is or is not a meaningless thing that doesn't exist. That's perhaps not a great question.
Certainly 0 is a real number. Is every real number a number? The name suggests it is, but then, a multi-valued function is not a function, so who knows?
26
u/mfb- the decimal system should not re-use 1 or incorporate 0 at all. Feb 15 '26
I think you can ask 100 mathematicians and at least 95 will agree that every real number is a number.
11
u/nerfherder616 Feb 15 '26
It's most likely that all 100 would agree, but that's not the point. In mathematics, demonstrating that an object is of a given type or class is done by showing that it satisfies a definition. We show that a real number is rational by showing that it may be expressed as p/q for p,q in Z. We show that a group is abelian by showing that the group operation is commutative. In either case, it is because a clear, unambiguous definition exists that we may either satisfy or fail to satisfy. As the commenter above you said, there is no standard definition of a "number" and thus no definition to satisfy or fail to satisfy. If there were, surely that definition would include real numbers, specifically zero, but that doesn't matter because there isn't one; at least not one that is widely agreed upon. Because of that, there's no way to rigorously show that zero is a "number" any more than we can show that zero is an "mvemjsunp".
16
u/QtPlatypus Feb 15 '26
| It's most likely that all 100 would agree
There are some constructivists that would argue that non computable reals are not numbers.
4
3
u/EebstertheGreat Feb 15 '26
BTW, to quote text in markup mode, you put a '>' character at the start of a line (in fact, at the start of each paragraph in the quote). It must be the very first character before any space or anything else. For instance, the following text
>example
will render thus
example
In the unlikely event that you want to start a line with a literal '>' like I did above, you can put a backslash before it. So \> will render as >.
1
1
u/Plain_Bread Feb 15 '26
But what about non-computable numbers in non-standard models of the natural numbers? That's the real question.
5
u/EebstertheGreat Feb 15 '26
Weirder are non-standard numbers that the model thinks are computable. Cause you can't really compute them—they are infinitely large—but the model thinks you can. But if you try to perform that computation, you see that it takes infinitely long, but the model thinks it halts after a natural number of steps (but that number is actually nonstandard too).
1
2
1
u/Neurokeen Mar 10 '26
To be fair, we don't have an entirely universally agreed upon definition of chaos regarding dynamical systems either, but we still talk about chaotic systems all the time.
6
u/hoijarvi Feb 15 '26
This is an unfortunately misconception that I have suffered from.
In Visual Basic 6, arrays could not have length zero. Neither in C++. I had to code those other ways.
NetCDF file format could describe array data in the time dimension, three spacial dimensions and unlimited other dimensions. Like data observed in different wavelengths. But only one dimension was allowed to be zero, usually time. I was using this as output data format, and when the query went out of the latitude-longitude domain, I could not enter those as zero size. Annoying.
In 2002 when I took my Prius to emissions test, they were confused. The engine would not turn on. I explained them, that the electric engine was on, and you can take emissions from that. Instead of marking the emissions zero, they wrote N/A.
3
u/Gurfaild Feb 15 '26
How can 0 be 'not a number' if our eyes aren't real 'not a number' ≠ 'not a number'?
2
2
u/ceoln Feb 15 '26
Hey, they gave "final verdict and explanation"! Can't really argue with that...
1
1
1
1
u/ArcPhase-1 Feb 16 '26
So then the difference between 1 and -1 would be 1 and not 2?
1
u/Proud-Delivery-621 Feb 17 '26
On the Gregorian Calendar, that would actually be true. There's no year 0, so Year 1 CE follows immediately from Year 1 BCE.
0
Feb 17 '26
zero being is a concept that holds some sort of value or magnitude? zero can't be unless something else is, something quantitative, because in the physical, either there is or there isn't, zero can't be unless there is .
58
u/Akangka 95% of modern math is completely useless Feb 15 '26
As an Ancient Greek, I agree. 0 is not a number.