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 Jul 11 awarded Necromancer Sep 8 awarded Good Question Jul 2 awarded Curious Jan 2 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.