@frobunnius This is exactly what I was looking for - thank you!
They’re just starting to learn about field homomorphisms and I was trying to find a good way to pin point that the isomorphisms we care about are structural, not cardinality based
Hi friends - I’m grading the following question for a class:
“If φ: ℚ(i) → ℚ(i) is a nonzero homomorphism, prove that it is an isomorphism.”
A couple students are using a size argument - “since φ is injective and these fields are the same size, it must be surjective”
Intuitively I don’t believe this is correct, however I’m self-doubting big time!
Would this be a correct argument?
(Please be nice, I’ve been sick for like 2 weeks and my brain is dead)
@doctor_jekel Thank you! Sadly the break will only be about a week long - January quals are right around the corner & I’ve got a paper that I meant to get out months ago 🫣
My dad literally hasn’t been to school since 1988 and he still has nightmares that he can’t find his locker or can’t remember the combination (he had one of these said nightmares last night)
Today I was told to be somewhere as close as possible to a certain time and I couldn’t tell if they didn’t want me to come early or if they didn’t want me to be late
But instead of asking that, I said “are we talking limit from the left or limit from the right”
Hi friends! I wanted to share that, in the midst of the Twitter decline, I’ve moved to Instagram! If you’d like to stay in touch, you can find me at @/rosetheoryy
In 2016, Lemke Oliver and Kannan Soundararajan discovered that if a prime number ends in a digit d, the next prime number after it is less likely to end with d. This holds in base 10 and base 3, and is conjectured to hold in every base.
Is there a database somewhere of questions that are good for Calculus quizzes/exams? I’m currently using my old textbooks but it would be sick if there was just a huge list somewhere separated by the type of questions one may be looking for