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May
23
awarded  Civic Duty
May
23
comment Why are particular combinations of algebraic properties “better” (richer and more pervasive) than others?
Also it seems to me like Voevodsky's pursuit of 2-theories was about breaking with category-theory like you say. In his IAS talk he says exploring so far outside what was already known made it much harder for him to prove things because his prior knowledge was less helpful.
May
23
comment Why are particular combinations of algebraic properties “better” (richer and more pervasive) than others?
I think this question of mine is maybe a little similar. Qiaochu mentions Poisson algebras, an interesting, naturally occurring mathematical-object I had never come across.
May
23
comment Why are particular combinations of algebraic properties “better” (richer and more pervasive) than others?
Well, I wouldn’t assume that what shows up by the second year of graduate school is there because it’s the most interesting. For example we teach undergraduates too much calculus and postgrads see too few spaces.
May
23
comment Why only two binary operations?
ias.edu/articles/2-theories ←feels like Voevodsky trying to break with this kind of pattern
May
23
comment A resource for learning p-adic numbers
Well, Serre's Course in Arithmetic treats them in chapter 2.
May
23
revised In (relatively) simple words: What is an inverse limit?
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May
23
revised In (relatively) simple words: What is an inverse limit?
this answer has stayed relevant for so long that the links have now changed!
May
23
suggested approved edit on In (relatively) simple words: What is an inverse limit?
May
22
answered In (relatively) simple words: What is an inverse limit?
May
21
comment Learning schemes
math.uiuc.edu/Macaulay2/Book/ComputationsBook/chapters/schemes/…
May
21
comment What is the use of scheme theory?
math.uiuc.edu/Macaulay2/Book/ComputationsBook/chapters/schemes/…
May
21
comment understanding of the “tensor product of vector spaces”
hitoshi.berkeley.edu/221a/tensorproduct.pdf
May
15
revised In what sense does $\sum_{k=0}^{\infty} 2^{2k} = - {1 \over 3}$?
added 190 characters in body
May
14
revised In what sense does $\sum_{k=0}^{\infty} 2^{2k} = - {1 \over 3}$?
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May
14
revised In what sense does $\sum_{k=0}^{\infty} 2^{2k} = - {1 \over 3}$?
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May
14
asked In what sense does $\sum_{k=0}^{\infty} 2^{2k} = - {1 \over 3}$?
May
3
comment Are there any interesting semigroups that aren't monoids?
@AlexanderKonovalov BTW, this is not my idea; it's the prologue of books.google.com/books?id=0ukzw5VszNwC.
May
3
comment Are there any interesting semigroups that aren't monoids?
@AlexanderKonovalov Well, the usual thing would be a finite-state automaton, but really you can treat a semigroup called $\mathrm{Time}$ as an index set and use that to parameterise any $X$ you’re interested in.
May
3
answered Are there any interesting semigroups that aren't monoids?