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21h
comment What is real $R$ so that every subset of Euclidean space with diameter one is inside a ball of radius $R$?
Such sets will be bounded by n-simplexes, and those lie in their circumscribed sphere. I had stated what is I think a wrong formula for those spheres' radius, but this is what will be your $R$. It will not be strictly less, just less than or equal. For $n=3$ (triangle), yes, $R=\sqrt{3}$.
22h
comment How to find a permutation of a specific rank?
How do you define the rank of a permutation?
1d
comment What does “maximum order elements to mod n” mean for a number n without primitive roots modulo n?
@iadvd: I don't think so. I'm not familiar with one (off-hand), but that doesn't mean that there couldn't be one I don't know. :)
1d
answered problem about symmetric positive semi-definite matrix
1d
revised Prob. 5 (a) in Supplementary Exercises in Munkres' TOPOLOGY, 2nd ed: How to show that this map is a homeomorphism?
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1d
revised Prob. 5 (a) in Supplementary Exercises in Munkres' TOPOLOGY, 2nd ed: How to show that this map is a homeomorphism?
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1d
comment Prob. 5 (a) in Supplementary Exercises in Munkres' TOPOLOGY, 2nd ed: How to show that this map is a homeomorphism?
I wrote up what's missing as it is too long as a comment.
1d
answered Prob. 5 (a) in Supplementary Exercises in Munkres' TOPOLOGY, 2nd ed: How to show that this map is a homeomorphism?
1d
comment Prob. 5 (a) in Supplementary Exercises in Munkres' TOPOLOGY, 2nd ed: How to show that this map is a homeomorphism?
You show that we have a continuous map $G \mapsto G/H$ (Agreed), then say "and the same argument shows that (the map in question) is continuous $G/H \mapsto G/H$". That is not true; you need an additional argument linking the two.
May
18
comment What does “maximum order elements to mod n” mean for a number n without primitive roots modulo n?
It's awesome that you come up with a conjecture relating to the goldbach conjecture, but that is a bit above my pay grade. :) @iadvd
May
18
comment A consequence of the inequality $\pi(x)+\pi(y)\ge\pi(x+y)$
I see. So disregard my second point; only the first still stands.
May
18
comment A consequence of the inequality $\pi(x)+\pi(y)\ge\pi(x+y)$
Note that the question asks only for which $n,m$ the inequality holds; it doesn't claim it hold for all such pairs. Note also that the weak inequality you claim to generally hold doesn't hold for all $n, m$: if you let $n=2, m=1$, you get $\pi(3-2) = 0, \pi(3)-\pi(2) = 2-1 =1$. These are just observations; I don't know how to show this.
May
18
revised prime number problem:
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May
18
revised prime number problem:
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May
18
answered prime number problem:
May
18
comment Are members of a diagonal positive definite matrix positive?
The answer is 'yes'. :)
May
18
revised What does “maximum order elements to mod n” mean for a number n without primitive roots modulo n?
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May
18
comment Are members of a diagonal positive definite matrix positive?
@Nofoos: I thought it was clear what you meant. If you follow the hint, you should see your result.
May
18
comment What does “maximum order elements to mod n” mean for a number n without primitive roots modulo n?
That's correct, as long as you mean the first such i, which is its order (I'm sure you mean that). Note that if $x^i = 1$ mod n, then $x^{i+kn}= 1$ mod n for any integer k, also $x^{2i} = (x^i)^2 = 1^2= 1$; etc.
May
18
comment Are members of a diagonal positive definite matrix positive?
What is $x^tAx$ when x is any standard basis vector?