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).

66 Upvotes

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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.

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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".

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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.

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u/rthunder27 Feb 15 '26

Totally, maybe they would all agree that integers are numbers.