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visits member for 1 year, 9 months
seen Jan 5 at 20:39

Sep
8
awarded  Good Question
Jul
2
awarded  Curious
Jan
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awarded  Yearling
Oct
9
awarded  Constituent
Oct
8
awarded  Caucus
Sep
19
comment Linear Algebra without Choice
you can still define a vector space to be finite dimensional if it is finitely generated. I think it is a basic theorem of linear algebra that such a vector space automatically has a (finite) basis, even without the axiom of choice.
Jul
6
comment When was the continuum hypothesis born?
what is Cantor's meaning of "Mannigfaltigkeiten" in this setting? surely it doesn't mean what we mean when we talk about manifolds.
Jun
5
awarded  Popular Question
Jun
4
asked for which truth-operations f can f-membership in a prime ideal be represented by a polynomial?
May
24
awarded  Nice Question
May
20
comment Objects which can't be defined without making choices but which end up independent of the choice
Nice. Is there a construction of this sort for $Tor$?
May
20
comment Objects which can't be defined without making choices but which end up independent of the choice
@Steven. actually in your example of Cauchy sequences there is no need to choose anything to define the sum of $A$ and $B$. You can just define the function $f\colon A\times B \to V$ defined by $f((x_n),(y_n))=(x_n+y_n)$. Then $A+B = Im(f)$ is nonempty if $A\times B$ is.
May
20
comment Objects which can't be defined without making choices but which end up independent of the choice
really? can't one just say $dim_k(V)$ is the smallest integer $n$ such that the set {$(v_1,\ldots,v_n)\in V^n\mid \langle v_1,\ldots, v_n\rangle=V$} is nonempty?
May
20
asked Objects which can't be defined without making choices but which end up independent of the choice
May
16
comment How to memorise (understand) Nakayama's lemma and its corollaries?
oh nice, thanks
May
16
comment How to memorise (understand) Nakayama's lemma and its corollaries?
I don't understand the last example. if you reduce that s.e.s. to $k$, you get an exact sequence $0\to 0\to k^n\to M\otimes k\to 0$. But we knew that already and you don't need flatness of M for that. How does it follow that in the original sequence $K$ vanishes?
May
14
answered Awfully sophisticated proof for simple facts
May
12
comment Magic trick based on deep mathematics
am I missing something or is $\sum_{g\in G}g$ always the unit element in the abelian group $(G,+)$?
May
9
comment A question in category theory
I would be interested whether there exists a counterexample if the isomorphism is not assumed natural. if C doesn't have to be abelian it is easy: Take C to be the category freely generated by two objects and two arrows between them (in different directions). Then for any $X$,$Y$ (possibly $X=Y$) in C we have $Hom(X,Y)\cong \aleph_0$, but the two objects in C are not isomorphic.
Apr
8
comment How long can this string of digits be extended?
Is there a good reason why N(b) can't be infinite?