Algebra 8 | Integers Modulo m ⤳ Abelian Group

[@albertovelasquez9027]

I am studying this on my own and you just drop this. Thanks!

[@Mathis-i5d]

the inverse [k] is [-k] obv., but wouldn’t it be better to write it as [m-k] since you defined the classes of equivalence going from 0 to m-1, which doesn’t include -k ?

[@brightsideofmaths]

Yes, [-k] = [m-k] = [2m-k]. We have infinitely many elements in an equivalence class and each of these can be used as a representative.

[@YouTube_username_not_found]

But you haven't proven that the modulo addition is well-defined or that [0] is the neutral element. Are you going to do that in another video?

[@brightsideofmaths]

We will do that in the general context :) (Both things are not so hard:)

[@YouTube_username_not_found]

@@brightsideofmaths OK 😎

[@mtarnowski95]

Why abuse the = sign in the title? Most abelian groups have nothing to do with integers.

[@brightsideofmaths]

Clickbait