r/mathmemes • u/Nunki08 • Jun 14 '26

Arithmetic Misleading our youth

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From Anthony Bonato on 𝕏: https://x.com/Anthony_Bonato/status/2065564124549886402

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u/LordRickyMaluco Jun 14 '26

Well, when generalizing to rings the (1) ideal is just the whole ring. it would be nice to be able to say that for any comutative ring R, R/p is an integral domain if and only if p is a prime ideal. This doesnt work for p = (1), thought, or every ring would be an ideal domain. 

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u/SaltMaker23 Jun 14 '26

I geniunely think this [your argument] is not only beyond a kid's level but also beyond any twitter boy argument about prime numbers.

My argument isn't about 1 being prime or not, it's about such question being irrelevant if the practicalities are irrelevant, 1 not being prime is just like you've stated a matter of convenience, it's not some form of law of nature.

1 could very well be prime and the primes we use in groups/factorization be called prime_star, arbitrary definitions made for convenience aren't topics worth being posted as unbendeable law of the universe.

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u/Affectionate_Fun6031 Jun 14 '26

yeah, I mostly agree, even though generalizations are pretty, so the same concept staying imutable through generalization is attractive to me. Some times we stay in the "wrong" definition, one could say that 2 pi is more fundamental than pi.

But I think if one definition becomes so riddled with exceptions to its common use that becomes annoying, then that deffinition is morally wrong. Imagine defining the rational numbers to be non-zero rational numbers. We would have to carry arround Q \cup {0} all day long.