fossilesque@mander.xyzM to Science Memes@mander.xyzEnglish · 7 天前I just cited myself.mander.xyzimagemessage-square239fedilinkarrow-up1852arrow-down143
arrow-up1809arrow-down1imageI just cited myself.mander.xyzfossilesque@mander.xyzM to Science Memes@mander.xyzEnglish · 7 天前message-square239fedilink
minus-squareSop@lemmy.blahaj.zonelinkfedilinkEnglisharrow-up24·7 天前That’s not an axiom or definition, it’s a consequence of the axioms that define arithmetic and can therefore be proven.
minus-squareJohnDClay@sh.itjust.workslinkfedilinkEnglisharrow-up3arrow-down7·7 天前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.
minus-squareJack Riddle@sh.itjust.workslinkfedilinkEnglisharrow-up7·7 天前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 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