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comment Solutions of $a^{2} - 2b^{2} \equiv 0$ mod $p$
Thank you very much! The terminology really helps when researching this!
comment Why is proof of the [topological] closed graph theorem incorrect?
Thanks; I see now there's nothing guaranteeing that $N$ can be be written as $U' \times V'$ with $U'$ definitely a subset of $U$. Can I fix this approach or am I off altogether? I could use some hints going forward because I'm pretty stumped.
comment Which is larger? $20!$ or $2^{40}$?
Guys, I think the point is that anyone could have plugged these numbers into their calculator in a second. Posters who ask questions like these usually have the implicit assumption that they want to prove it elegantly without explicit computation - for novelty purposes.
comment How can I better understand manipulating “operators” in mathematical relations?
Thanks. Okay, I understand that you can do this algebra of functions, but if I just have some operator or map $A : U \rightarrow V$ and I have an element $u \in U$, then when I write $Au$ I mean the result of applying operator $A$ with input $u$? Is writing the operator next to a member of its input type "implied application"?
comment What “is” a matrix in the context of a vector space?
I think I understand. Since the space of ALL possible linear maps from V to W is isomorphic with the set of ALL m x n matrices, we can work with matrices and perform arithmetic on them and interpret our results in terms of linear mappings because of the isomorphism. So would it be reasonable then to view the "multiplication" of a vector by a matrix just an expression of the matrix's corresponsing map being applied to the vector? I think I'm splitting hairs at this point but I do feel more comfortable thanks to your post.
comment Two questions about Euler's number $e$
If I may recommend a book, check out "e: The story of a number" by Eli Maor. It's an excellent read that talks all about the history of the number e and all of its implications. You can find it here (or of course look for it at a library at school or otherwise):
comment Are these 2 graphs isomorphic?
I would be interested in seeing the code, if you don't mind.
comment Notation for factorial-type pattern with a skip/step of two instead of one?
Well... that is indeed what I was looking for. Didn't know that notation existed!