Matthew Salomone, your videos are really great! little note: in this video at 5:23 you say: alfa = Pi^2 satisfy t^2 - Pi = 0 it must be alfa =sqrt(Pi) satisfy t^2 - Pi = 0 I think then you can also say Pi is algebraic over R: it satisfies t^2 - Pi^2=0. But Pi should be transcendental. So we can only speak about algebraic over Q and not over R.
I agree that the number alpha was probably supposed to be sqrt(pi), but as far as labelling things as algebraic, why would that only be restricted to Q and not R?
I've never encountered anyone / text that's bothered properly explaining algebraic vs transcendental before. But it did take 1.5 Abstract Algebra to get here, so the 'price of admission' is very steep.
I knew the rationals were countable, but didn't even consider the countability of the algebraic numbers before. Very interesting stuff!
Baby Rudin chapter 2 has a problem about this! Super cool proof. (Unexpected from an analysis book to have such an algebraic result :p )
@@selahw2609 Oh that's cool!
This guys is probably the best lecturer I’ve seen on RUclips. 👏🏻
I think he's right up there with Professor Dave and Sal Khan, and for me, Matt's puns and wackiness are the icing on the cake!
Greetings from India Matthew. Your 20 mins of one video is really worth attending 1 month of algebraic structures class. God bless you
How are things going in India, and how did your algebraic structures class go overall?
Matthew Salomone, your videos are really great!
little note:
in this video at 5:23 you say: alfa = Pi^2 satisfy t^2 - Pi = 0
it must be alfa =sqrt(Pi) satisfy t^2 - Pi = 0
I think then you can also say Pi is algebraic over R: it satisfies t^2 - Pi^2=0.
But Pi should be transcendental. So we can only speak about algebraic over Q and not over R.
Your first point is correct. As to your second point, pi is algebraic over R, because it satisfies the polynomial x - pi = 0.
I agree that the number alpha was probably supposed to be sqrt(pi), but as far as labelling things as algebraic, why would that only be restricted to Q and not R?
In 12:28, the "this always works" theorem, are we suppose to have that k
Yes, because otherwise there would be no reason to introduce "k" ("n" would be sufficient). So k less or equal n-1. I hope the professor can confirm.
Thank you so much!
Tiny note ... I think you meant the square root of pi instead of pi squared.
Great videos though!
Who eats square pies anyways.
Your videos are great too Bill Shillito ....
12:00 you can prove k=n-1 if p is irreducible.
I've never encountered anyone / text that's bothered properly explaining algebraic vs transcendental before. But it did take 1.5 Abstract Algebra to get here, so the 'price of admission' is very steep.
xd pi² doesn't satisfy t²-pi=0, +-sqrt(pi) does
Good catch!