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Apr
11
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.
Apr
10
asked Why is proof of the [topological] closed graph theorem incorrect?
Nov
12
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.
Oct
14
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"?
Oct
14
asked How can I better understand manipulating “operators” in mathematical relations?
Jul
8
accepted What “is” a matrix in the context of a vector space?
Jul
8
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.
Jul
8
asked What “is” a matrix in the context of a vector space?
May
31
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): amazon.com/Story-Number-Princeton-Science-Library/dp/0691141347
May
16
comment Are these 2 graphs isomorphic?
I would be interested in seeing the code, if you don't mind.
Apr
23
awarded  Critic
Aug
22
asked What are the technical reasons that we must define vectors as “arrows” and carefully distinguish them from a point?
Mar
28
awarded  Scholar
Mar
28
accepted Notation for factorial-type pattern with a skip/step of two instead of one?
Mar
28
awarded  Supporter
Mar
28
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!
Mar
28
awarded  Student
Mar
28
awarded  Editor
Mar
28
revised Notation for factorial-type pattern with a skip/step of two instead of one?
added 146 characters in body
Mar
28
asked Notation for factorial-type pattern with a skip/step of two instead of one?