PSE Lectures - Ep 4 - Groups (3/4)

In this session is focused on the concepts of homomorphism and isomorphism in groups.

[MrCoreyTexas]

I've seen the backwards e (there exists) and upside down a (for all), but I wasn't familiar with backwards e followed by "!". I take it "!" is unique, because of what you said at 1:13:25

[MrCoreyTexas]

I was very confused by the example at 1:07:00 until I worked out some stuff on paper. I don't have a proof, but it seems that (x mod nm) mod n == x mod n. Since n divides nm, the dual mods reduce to just mod n.

Whereas (x mod nm+1) mod n != x mod n. Since n does not divide nm+1, the modulus does not reduce.

so you have a mod of a mod on the domain, since when you evaulate f(x+y mod mn) that in itself gets mod n'd. I'd never thought about what happens when you "mod a mod" before, I haven't seen any examples in the math I've studied.

[MrCoreyTexas]

at 28:41 you meant to wrote q(xx') = xx'H, and you left out the prime symbol

[MrCoreyTexas]

Got confused at 1:37:00 again when you went from f(x)=f(y) to f(xy^-1)=e. I think you are leaving out steps and you confuse your listeners

[MrCoreyTexas]

never heard anyone call sine sinus and cosine cosinus