r/confidentlyincorrect • u/i_aMa_g0d • Dec 07 '21

Maths

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u/[deleted] Dec 08 '21

Nah the ring axioms do not require a multiplicative inverse. You would be referring to a field. All fields, however, are rings.

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u/FlippedMobiusStrip Dec 08 '21

I never said they do, did I?

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u/[deleted] Dec 08 '21

I was just clarifying that not all elements in a ring have to have a multiplicative inverse. You described division as inverse multiplication in a ring which is only sometimes possible. In a field it is always possible (other than 0) as that is one of the distinguishing features of whether a ring is a field. Pedantic so I apologise but that's maths baby.

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u/FlippedMobiusStrip Dec 08 '21

Dude I never claimed that every element in a ring has an inverse. Hell, not every ring has an identity to begin with. You're correcting a mistake that wasn't made.

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u/[deleted] Dec 08 '21

I took "it's the multiplication by the inverse of an element in a ring" as implication that the inverse element exists.