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1m
answered Is there such thing as an unnormed vector space?
5h
awarded  Constituent
11h
comment A question on Weyl algebra $A_1$
$d^2$ cannot be in the kernel, since $d^2$ is not an element of $A_1^2$.
11h
comment how to show $\mathbf{Q} $ is not free
You can use the fact that all f.g. subgroups are cyclic. It the thing were free, it woud have a basis. That basis cannot have two elements because the subgroup generated by two lements is cyclic and $\mathbb Z^2$ is not isomorphic to $\mathbb Z$.
11h
comment how to show $\mathbf{Q} $ is not free
But it could be free and non-finitely generated! :-)
23h
comment Difference between cellular and simplicial homology
Every simplicial decomposition of a space is a cellular decomposition, and then the simplicial homology and the cellular homology are exactly the same (but not conversely; it is often the case that spaces have much more efficient cellular decomposition that triangulations)
1d
awarded  Good Answer
1d
comment $c_o$ is not isometric to $c_0 \oplus c_0$
Please double- or triple- check your posts for typos.
2d
comment $C_c(\mathbb R^n)$ is not dense in $\mathcal L^\infty(\mathbb R ^n)$
No, it is not true that $\lVert\phi_n\rVert_\infty=0$. In any case, you can proceed simply by showing that the distance between your $f=1$ and any $\phi\in C_c$ is at least one.
2d
answered $C_c(\mathbb R^n)$ is not dense in $\mathcal L^\infty(\mathbb R ^n)$
2d
comment Why do we write $a^n$ instead of $^n\!a$ for exponentiation?
You should browse Cajori's History of Mathematical Notations.
2d
comment An entire and one-to-one function must be of the form AZ+B, A non-zero. How to rule out higher degree polynomials in z?
No even degree polynomial is one to one, in fact. (Odd-degreee polynomials of degree different to one are not much better in that respect!)
2d
comment An entire and one-to-one function must be of the form AZ+B, A non-zero. How to rule out higher degree polynomials in z?
This has surely been asked already on the site.
2d
comment Why is the axiom of choice not taught from the start to mathematics undergraduates?
The difficulty students face at that point is in organizing a proof by induction, or in the noncommutativity of quantifiers, n what it means exactly that a limit does not exist, and so on. Constructivity cannot be more than an anecdote.
2d
comment Why is the axiom of choice not taught from the start to mathematics undergraduates?
@AsafKaragila, I can only infer that you have never taught one-variable calculus. Any discussion on dependent choice in the middle of a proof of the fact that continuity and sequential continuity are equivalent will be lost except of a 1% of your audience, except in extraordinarily exceptional circumstances.
2d
comment Show $ \{ (\xi,\eta,\zeta) \in \mathbb{R^3} : \xi = \eta = \zeta \}$ is closed
@DanielKelsall, you can add extra {}{}{}{}{}{}{} to some formula to get pass character count limits. You did not hear this from me...
2d
comment Differentiable manifolds that allow isometric transition maps.
IIn your comment and in your edit you are using the word «isomorphic» but you probably mean something else.
2d
comment Why is the axiom of choice not taught from the start to mathematics undergraduates?
Notice that emphasizing this in a course on set theory, naive or not, is of course rather reasonable :-)
2d
comment Differentiable manifolds that allow isometric transition maps.
I don't understand what you mean by «transition maps are isometric».
2d
comment Why is the axiom of choice not taught from the start to mathematics undergraduates?
That's in the remaining 25%. (Essentially?) all of that is covered by Zorn's lemma, and there is no need to dwell on why exactly the lemma is equivalent to AC or to involve any axiomatic set theory at all. Of course, one should mention somewhat in passing that there is such a thing as axiomatic set theory, that the lemma is equivalent to the nonvanishing of appropriate cartesian products, why that is called 'choice' and so on. But from that to telling calculus students that the equivalence of continuity to continuity by sequences is even related from afar to AC is absurd.