Question

Show that if there is a function $g:Y\to X$ such that $g\circ f$ is the identity function on $X$, then $f$ is one to one.

score 195 · Answer 1 · 2015-09-01 00:52:56

195

Views

Show that if there is a function $g:Y\to X$ such that $g\circ f$ is the identity function on $X$, then $f$ is one to one.

Published on 01 Sep 2015 - 0:52

score 1.1k · Answer 2 · 2026-03-29 23:24:53

1.1k

Views

Alternative proof of the Riemann Sum Theorem using Mean Value Theorem for Integrals.

Published on 29 Mar 2026 - 23:24

score 94 · Answer 3 · 2015-09-05 04:57:02

94

Views

(ZF - Foundation) proves that $\log_2$ can't be infinitely iterated: Alternative proof

Published on 05 Sep 2015 - 4:57

score 434 · Answer 4 · 2015-09-06 10:27:52

434

Views

Different ways of Proving the existence of Tensor Product

Published on 06 Sep 2015 - 10:27

score 44 · Answer 5 · 2015-09-11 04:55:24

44

Views

Proof of $\lim_{k\to \infty}{|x^k-x|\over { 1+|x^k-x|}}=0$

Published on 11 Sep 2015 - 4:55

score 327 · Answer 6 · 2026-04-03 05:48:06

327

Views

The value of $\gcd(2^n-1, 2^m+1)$ for $m < n$

Published on 03 Apr 2026 - 5:48

score 209 · Answer 7 · 2015-09-17 09:22:06

209

Views

Contractions of maximal ideals in finite type $K$-algebras

Published on 17 Sep 2015 - 9:22

score 63 · Answer 8 · 2015-09-19 12:49:05

63

Views

Show that $[a,b] \subset Range(f)$

Published on 19 Sep 2015 - 12:49

score 593 · Answer 9 · 2015-09-21 19:03:33

593

Views

Showing that a wave equation $u_{tt}=ku_{xx}$ has solution $u=0$ if $u(x,0)=u_t(x,0)=0$

Published on 21 Sep 2015 - 19:03

score 35 · Answer 10 · 2026-04-01 16:23:55

35

Views

Show that $[H,K,L] = A_5$, where $H,K,L$ have order $2$.

Published on 01 Apr 2026 - 16:23

score 89 · Answer 11 · 2015-09-25 10:08:11

89

Views

Synthetic proof of a bisector length

Published on 25 Sep 2015 - 10:08

score 60 · Answer 12 · 2015-09-25 18:23:33

60

Views

Prove that $x\cdot y=0 \iff x=0$ or $y=0$ without cases

Published on 25 Sep 2015 - 18:23

score 862 · Answer 13 · 2015-09-29 13:14:56

862

Views

$T:X\to Y$ a linear operator, $Y$ finite-dimensional, then $\ker T$ is closed iff $T$ is continuous

Published on 29 Sep 2015 - 13:14

score 177 · Answer 14 · 2026-04-03 08:43:08

177

Views

Elementary theorems that require AC

Published on 03 Apr 2026 - 8:43

score 252 · Answer 15 · 2015-09-30 22:49:47

252

Views

A combinatorial proof of $\forall n\in\mathbb{N},\,\binom{n}{2}=\frac{n(n-1)}{2}$

Published on 30 Sep 2015 - 22:49

List Question

Show that if there is a function $g:Y\to X$ such that $g\circ f$ is the identity function on $X$, then $f$ is one to one.

Alternative proof of the Riemann Sum Theorem using Mean Value Theorem for Integrals.

(ZF - Foundation) proves that $\log_2$ can't be infinitely iterated: Alternative proof

Different ways of Proving the existence of Tensor Product

Proof of $\lim_{k\to \infty}{|x^k-x|\over { 1+|x^k-x|}}=0$

The value of $\gcd(2^n-1, 2^m+1)$ for $m < n$

Contractions of maximal ideals in finite type $K$-algebras

Show that $[a,b] \subset Range(f)$

Showing that a wave equation $u_{tt}=ku_{xx}$ has solution $u=0$ if $u(x,0)=u_t(x,0)=0$

Show that $[H,K,L] = A_5$, where $H,K,L$ have order $2$.

Synthetic proof of a bisector length

Prove that $x\cdot y=0 \iff x=0$ or $y=0$ without cases

$T:X\to Y$ a linear operator, $Y$ finite-dimensional, then $\ker T$ is closed iff $T$ is continuous

Elementary theorems that require AC

A combinatorial proof of $\forall n\in\mathbb{N},\,\binom{n}{2}=\frac{n(n-1)}{2}$

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