this post was submitted on 27 Jun 2024
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That’s not an axiom or definition, it’s a consequence of the axioms that define arithmetic and can therefore be proven.
There are versions of math where that isn't true, with infinitesimals that are not equal to zero. So I think it is an axium rather than a provable conclusion.
Those versions have different axioms from which different things can be proven, but we don't define 9.9 repeating as 1
That's not what "axiom" means