• Sop@lemmy.blahaj.zone
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    5 months ago

    That’s not an axiom or definition, it’s a consequence of the axioms that define arithmetic and can therefore be proven.

    • JohnDClay@sh.itjust.works
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      5 months ago

      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.

      • Jack Riddle@sh.itjust.works
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        5 months ago

        Those versions have different axioms from which different things can be proven, but we don’t define 9.9 repeating as 1