Why is Z_q not a field when q is, say, 4?

the very basic example is that say if you have Z_4, the polynomial "2" does not have a multiplicative inverse

Ohh

Neat

Z_4 is not a field because 2 does not have a multiplicative inverse

Yeah haha been a while

and since Z_q is a subfield of F_q[x]

yeah I've literally pullen out my abstract alg. book out today

i need some cryptography knowledge from it

i learned all of this again today 😛

That's neat. I enjoyed abstract algebra but mostly only needed the linear algebra part since then (11 years ago). Rotation groups and some other stuff relevant to geometry, but not much more. Cryptography seems interesting, we did cover RSA at some point, I only remember the main idea, that factoring is hard 😁

@ThisIsChris wellyeah, some pajeets found a way to crack RSA with you guessed it, Galois fields

Is that a recent thing?

yeah

like a year or so

it's amazing how irrelevant Abstract Algebra used to be until computers, and now it's hella important

Huh no kidding. Guess I better put 2FA on my bank accounts then

yep

idk about you, my dad make me take applied math

it was "fun" i guess, but I really want to go back to college and get a pure math degree

later

😛

pure math is so much more fun that learning about how to earn money at google

"pure math is fun" I will never understand you types

https://giphy.com/gifs/frog-get-out-U9DiGJDKfbwGY

@Deleted User

@ThisIsChris

I'll stop there

@YourFundamentalTheorum haha I like the sigma algebra one but don't get the epic one? It's a true statement if f is 1-1 and onto. Not sure what else.

@ThisIsChris epic means an epimorphism

which is literally defined by that equation

so f is epic

https://en.wikipedia.org/wiki/Epimorphism

So this Julian Von Abele's phsyics QCI theory of physics- anyone think anything of it?

@Jonaltright I'm thinking of buying the book to support him, I don't really know what his theory is. I did take a physics class in college so I hope I can understand something of it 😁

Yeah I saw people doing that. I'm sure they'll suspend publication once they see an uptick in sales though :(

Hopefully he makes out ok. Doxxing has been devastating for me

@ThisIsChris Physics classes can be harsh. I took some to fulfill return requirements for a computer science degree. Are they actually useful in your career?

@Jacob Some intro to physics is a "now to know" but not "need to know". The main use in my career has been to better understand some calculus concepts, since the beginnings of calculus and physics are tightly connected.