Question

How to prove surjectivity of $f:\{1,\ldots,n\}\to\Bbb Z_n,\,k\mapsto[k]$? Alternative proofs for $|\Bbb Z_n|=n$?

score 61 · Answer 1 · 2016-09-25 19:25:54

61

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How to prove surjectivity of $f:\{1,\ldots,n\}\to\Bbb Z_n,\,k\mapsto[k]$? Alternative proofs for $|\Bbb Z_n|=n$?

Published on 25 Sep 2016 - 19:25

score 286 · Answer 2 · 2016-09-28 12:04:02

286

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$X$ is Tychonoff with some properties of continuous extension of function on $X$, how can we show $X$ is normal?

Published on 28 Sep 2016 - 12:04

score 92 · Answer 3 · 2016-09-29 17:13:46

92

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Solving $\lim\limits_{x \to 0} \frac{\ln(1+x)}{\ln(1+4x+x^2)}$ without L'Hospital or Sandwiching

Published on 29 Sep 2016 - 17:13

score 316 · Answer 4 · 2016-10-02 04:10:42

316

Views

Coordinate free proof of height of intersection of two triangles with common base

Published on 02 Oct 2016 - 4:10

score 160 · Answer 5 · 2016-10-03 21:18:26

160

Views

Proving algebraically $a^2+b^2\ge a^{\alpha}b^{2-\alpha}$ for $0\le\alpha\le2$ and $a,b\ge0$

Published on 03 Oct 2016 - 21:18

score 1.2k · Answer 6 · 2026-03-28 14:55:12

1.2k

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If $\mathfrak{Y}$ is a closed subspace of a reflexive Banach space $\mathfrak{X}$, then is $\mathfrak{Y}$ reflexive too?

Published on 28 Mar 2026 - 14:55

score 1.2k · Answer 7 · 2016-10-06 01:20:31

1.2k

Views

Proving the Alternate Series Test with Monotone Convergence

Published on 06 Oct 2016 - 1:20

score 213 · Answer 8 · 2026-03-29 12:40:25

213

Views

Prove that if a sequence $a_{n}$is not a Cauchy sequence then: a) or b)

Published on 29 Mar 2026 - 12:40

score 140 · Answer 9 · 2016-10-06 14:56:57

140

Views

Working out which line a number is on in a Floyd's Triangle

Published on 06 Oct 2016 - 14:56

score 121 · Answer 10 · 2016-10-08 16:05:20

121

Views

Reference request: analytic proof of the Ascoli-Arzelà theorem

Published on 08 Oct 2016 - 16:05

score 574 · Answer 11 · 2026-03-30 05:36:31

574

Views

Proof about divisibility and greatest common divisor that doesn't use Bezout's formula

Published on 30 Mar 2026 - 5:36

score 456 · Answer 12 · 2016-10-09 16:10:54

456

Views

How to use well-ordering principle of natural numbers to prove that $S_n = \frac{n(n+1)}{2}$?

Published on 09 Oct 2016 - 16:10

score 712 · Answer 13 · 2016-10-11 02:25:13

712

Views

Let $d_1(x,y)=|x-y|$ and $d_2(x,y)=|\frac1x-\frac 1y|$. Prove that $d_1$ and $d_2$ are equivalent in $(0,1)$

Published on 11 Oct 2016 - 2:25

score 1.1k · Answer 14 · 2016-10-14 02:21:11

1.1k

Views

Prove that F $\subseteq$ R is closed if and only if every Cauchy sequences contained in F has a limit that is also an element of F.

Published on 14 Oct 2016 - 2:21

score 233 · Answer 15 · 2016-10-14 16:01:07

233

Views

$(E,\|.\|)$ is complete $\iff$ every normally convergent series is convergent.

Published on 14 Oct 2016 - 16:01

List Question

How to prove surjectivity of $f:\{1,\ldots,n\}\to\Bbb Z_n,\,k\mapsto[k]$? Alternative proofs for $|\Bbb Z_n|=n$?

$X$ is Tychonoff with some properties of continuous extension of function on $X$, how can we show $X$ is normal?

Solving $\lim\limits_{x \to 0} \frac{\ln(1+x)}{\ln(1+4x+x^2)}$ without L'Hospital or Sandwiching

Coordinate free proof of height of intersection of two triangles with common base

Proving algebraically $a^2+b^2\ge a^{\alpha}b^{2-\alpha}$ for $0\le\alpha\le2$ and $a,b\ge0$

If $\mathfrak{Y}$ is a closed subspace of a reflexive Banach space $\mathfrak{X}$, then is $\mathfrak{Y}$ reflexive too?

Proving the Alternate Series Test with Monotone Convergence

Prove that if a sequence $a_{n}$is not a Cauchy sequence then: a) or b)

Working out which line a number is on in a Floyd's Triangle

Reference request: analytic proof of the Ascoli-Arzelà theorem

Proof about divisibility and greatest common divisor that doesn't use Bezout's formula

How to use well-ordering principle of natural numbers to prove that $S_n = \frac{n(n+1)}{2}$?

Let $d_1(x,y)=|x-y|$ and $d_2(x,y)=|\frac1x-\frac 1y|$. Prove that $d_1$ and $d_2$ are equivalent in $(0,1)$

Prove that F $\subseteq$ R is closed if and only if every Cauchy sequences contained in F has a limit that is also an element of F.

$(E,\|.\|)$ is complete $\iff$ every normally convergent series is convergent.

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