Question

What is a formal full proof that "$ \mathbf{Set}$ is a Category" in the context of Category Theory?

score 1.3k · Answer 1 · 2018-11-11 18:39:39

1.3k

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What is a formal full proof that "$ \mathbf{Set}$ is a Category" in the context of Category Theory?

Published on 11 Nov 2018 - 18:39

score 41 · Answer 2 · 2018-11-11 20:51:39

41

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If the set of all upper bounds of $A$ and $B$ are equal and $\sup A$ exists, then $\sup B$ exists and $\sup A=\sup B$.

Published on 11 Nov 2018 - 20:51

score 165 · Answer 3 · 2018-11-11 23:34:50

165

Views

Finding the unconditional distribution of a binomial distribution

Published on 11 Nov 2018 - 23:34

score 61 · Answer 4 · 2026-03-25 23:19:53

61

Views

Limit of sequence $x_n$

Published on 25 Mar 2026 - 23:19

score 471 · Answer 5 · 2026-03-25 17:40:39

471

Views

Is it possible to prove Fubini’s Theorem without Dynkin’s Theorem or the Monotone Class Theorem?

Published on 25 Mar 2026 - 17:40

score 70 · Answer 6 · 2018-11-12 13:21:59

70

Views

Radius of convergence of power series $\sum_{n=1}^{\infty}\frac{1}{(1+\frac{1}{n})^{n^2}}x^{6n+2}$

Published on 12 Nov 2018 - 13:21

score 831 · Answer 7 · 2026-03-26 09:18:04

831

Views

Prove that, the function $f$ is injective: $f \big(f(x)f(y)\big) + f(x +y) = f(xy).$

Published on 26 Mar 2026 - 9:18

score 39 · Answer 8 · 2026-03-26 09:27:05

39

Views

Laurent series $f(z)=\frac{\sqrt{z}}{z+i}$

Published on 26 Mar 2026 - 9:27

score 132 · Answer 9 · 2026-03-26 06:29:56

132

Views

Equivalence of all representations of $\exp$

Published on 26 Mar 2026 - 6:29

score 56 · Answer 10 · 2018-11-17 13:39:04

56

Views

Alternative proof for existence of nth roots

Published on 17 Nov 2018 - 13:39

score 639 · Answer 11 · 2026-03-26 01:14:32

639

Views

Prove that the Cantor set is homeomorphic to $(X,\mathscr T)$.

Published on 26 Mar 2026 - 1:14

score 808 · Answer 12 · 2018-11-17 19:02:02

808

Views

How to check if a function is injective and surjective

Published on 17 Nov 2018 - 19:02

score 166 · Answer 13 · 2026-03-22 08:00:19

166

Views

$M$ is a point in an equalateral $ABC$ of area $S$. $S'$ is the area of the triangle with sides $MA,MB,MC$. Prove that $S'\leq \frac{1}{3}S$.

Published on 22 Mar 2026 - 8:00

score 1.1k · Answer 14 · 2026-03-27 00:02:55

1.1k

Views

Derivation of formula for surface integral

Published on 27 Mar 2026 - 0:02

score 31 · Answer 15 · 2026-03-25 01:21:16

31

Views

Error in expression of incomplete zeta function?

Published on 25 Mar 2026 - 1:21

List Question

What is a formal full proof that "$ \mathbf{Set}$ is a Category" in the context of Category Theory?

If the set of all upper bounds of $A$ and $B$ are equal and $\sup A$ exists, then $\sup B$ exists and $\sup A=\sup B$.

Finding the unconditional distribution of a binomial distribution

Limit of sequence $x_n$

Is it possible to prove Fubini’s Theorem without Dynkin’s Theorem or the Monotone Class Theorem?

Radius of convergence of power series $\sum_{n=1}^{\infty}\frac{1}{(1+\frac{1}{n})^{n^2}}x^{6n+2}$

Prove that, the function $f$ is injective: $f \big(f(x)f(y)\big) + f(x +y) = f(xy).$

Laurent series $f(z)=\frac{\sqrt{z}}{z+i}$

Equivalence of all representations of $\exp$

Alternative proof for existence of nth roots

Prove that the Cantor set is homeomorphic to $(X,\mathscr T)$.

How to check if a function is injective and surjective

$M$ is a point in an equalateral $ABC$ of area $S$. $S'$ is the area of the triangle with sides $MA,MB,MC$. Prove that $S'\leq \frac{1}{3}S$.

Derivation of formula for surface integral

Error in expression of incomplete zeta function?

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