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Feb
7
answered Showing the group in $\Bbb R$
Feb
5
revised Any necessary and sufficient condition(s) for closure of an open ball to be the corresponding closed ball?
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Feb
5
comment Any necessary and sufficient condition(s) for closure of an open ball to be the corresponding closed ball?
Ah, good point. The right condition would be that every point in the range is a limit of an increasing sequence.
Feb
5
revised Any necessary and sufficient condition(s) for closure of an open ball to be the corresponding closed ball?
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Feb
5
revised Any necessary and sufficient condition(s) for closure of an open ball to be the corresponding closed ball?
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Feb
5
answered Any necessary and sufficient condition(s) for closure of an open ball to be the corresponding closed ball?
Feb
4
revised Bijection bewteen $(-1,1)$ and $\{(x,y)\in\mathbb{R}^2:y=x^3\}$
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Feb
4
revised Bijection bewteen $(-1,1)$ and $\{(x,y)\in\mathbb{R}^2:y=x^3\}$
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Feb
4
comment Quotient Ideal, quick equivalence.
You probably meant to write $\langle x \rangle$ etc, not $<$. Triangular brackets are different from inequality signs (to write the former, use \langle, \rangle), and treating them the same makes everything much harder to read. Also, what do you mean by those brackets in the first place?
Feb
3
comment How are simple groups the building blocks?
@JohnDoe: Good. But I think Stefan's answer says more or less all I wanted to say about the subject, and the answers he links probably say all there is to say beyond that, without getting too technical (and I don't even have the expertise to get technical).
Feb
1
comment Closed ideals in $\mathbb B(H)$
What dimension do you have in mind? And isn't this $\alpha$ just $\aleph_0$?
Jan
30
comment How are simple groups the building blocks?
@JohnDoe: ping me tomorrow. I am myself curious about whether or not there is a better answer, and I don't want to deter others by making this question answered.
Jan
30
comment How are simple groups the building blocks?
@GregoryGrant: ${\bf Z}/4{\bf Z}$ is not the direct product of ${\bf Z}/2{\bf Z}$, but it is an extension of ${\bf Z}/2{\bf Z}$ by ${\bf Z}/2{\bf Z}$.
Jan
30
comment How are simple groups the building blocks?
As far as I know, this "making up" refers to the composition series. Every finite group has unique composition series, in which the factors are simple groups. These factors alone do not determine the group uniquely (far from it, actually), but they do allow us to write every finite group as the result of successive extensions by simple groups, starting from the trivial group. There may be some more content to it, so I will refrain from posting this as an answer (not being a specialist).
Jan
24
comment How to prove $\mathbb{N}\subseteq\mathbb{R}$ given basic field axiomatisation.
How do you prove that such a field contains ${\bf Q}$ without first (or simultaneously) proving that it contains ${\bf N}$?
Jan
24
comment How to prove $\mathbb{N}\subseteq\mathbb{R}$ given basic field axiomatisation.
How do you define ${\bf N}$?
Jan
24
revised How to prove $\mathbb{N}\subseteq\mathbb{R}$ given basic field axiomatisation.
edited title
Jan
19
comment Why do I get one extra wrong solution?
Wait, isn't $-1$ a square root of $1$?
Jan
19
answered Topologically-equivalent/metrically-equivalent metrics and the same topology
Jan
19
revised Relative postion of a plane and a hyperplane in $\mathbb{R^4}$
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