Question

How do you prove that if a set is countably infinite, then there exists a bijection between from the natural numbers to the set?

score 100 · Answer 1 · 2026-04-14 00:56:25

100

Views

How do you prove that if a set is countably infinite, then there exists a bijection between from the natural numbers to the set?

Published on 14 Apr 2026 - 0:56

score 848 · Answer 2 · 2026-04-15 04:46:20

848

Views

Prove that the set of Algebraic Numbers is countable.

Published on 15 Apr 2026 - 4:46

score 264 · Answer 3 · 2026-04-09 11:58:34

264

Views

Characterisation of equivalent metrics

Published on 09 Apr 2026 - 11:58

score 392 · Answer 4 · 2026-04-17 06:20:11

392

Views

Proving $\sqrt{2}$ is irrational

Published on 17 Apr 2026 - 6:20

score 72 · Answer 5 · 2026-04-14 21:41:08

72

Views

How can I mimic the given proof?

Published on 14 Apr 2026 - 21:41

score 165 · Answer 6 · 2026-04-11 05:37:03

165

Views

Can I prove a numerical inequality by manipulating it and ending at a true statement?

Published on 11 Apr 2026 - 5:37

score 74 · Answer 7 · 2026-04-09 15:17:02

74

Views

Divisiblity proof with coprimes of 6

Published on 09 Apr 2026 - 15:17

score 76 · Answer 8 · 2026-04-15 18:35:09

76

Views

Establish the convergence and find the limit of $a_n$

Published on 15 Apr 2026 - 18:35

score 178 · Answer 9 · 2026-04-14 11:24:22

178

Views

Help to improve or give a better proof that every non-negative measurable function can be written as a sequence of simple functions

Published on 14 Apr 2026 - 11:24

score 900 · Answer 10 · 2026-04-14 09:54:33

900

Views

How do I prove that there is a non-zero vector in the intersection?

Published on 14 Apr 2026 - 9:54

score 925 · Answer 11 · 2026-04-13 14:43:51

925

Views

Understanding a proof that, for $\varepsilon>0$, a set of finite measure is the disjoint union of sets of measure at most $\varepsilon$

Published on 13 Apr 2026 - 14:43

score 59 · Answer 12 · 2026-04-15 20:28:54

59

Views

Prove the surjectivity of $\nu(r,m) = 2^{r+1}m + \frac{2^{r}(3-2(-1)^{r})-1}{3}$ to $2 \mathbb{N}+1$

Published on 15 Apr 2026 - 20:28

score 186 · Answer 13 · 2026-04-12 09:43:44

186

Views

Set Theory Proof Practice Problem Help [CONFUSED]

Published on 12 Apr 2026 - 9:43

score 872 · Answer 14 · 2026-04-15 17:09:57

872

Views

Prove that every measurable set $E \subset \mathbb{R}$ is the union of a Borel set and a set of measure 0(2)

Published on 15 Apr 2026 - 17:09

score 254 · Answer 15 · 2026-04-13 08:57:49

254

Views

equipollent couple of points to define vectors

Published on 13 Apr 2026 - 8:57

List Question

How do you prove that if a set is countably infinite, then there exists a bijection between from the natural numbers to the set?

Prove that the set of Algebraic Numbers is countable.

Characterisation of equivalent metrics

Proving $\sqrt{2}$ is irrational

How can I mimic the given proof?

Can I prove a numerical inequality by manipulating it and ending at a true statement?

Divisiblity proof with coprimes of 6

Establish the convergence and find the limit of $a_n$

Help to improve or give a better proof that every non-negative measurable function can be written as a sequence of simple functions

How do I prove that there is a non-zero vector in the intersection?

Understanding a proof that, for $\varepsilon>0$, a set of finite measure is the disjoint union of sets of measure at most $\varepsilon$

Prove the surjectivity of $\nu(r,m) = 2^{r+1}m + \frac{2^{r}(3-2(-1)^{r})-1}{3}$ to $2 \mathbb{N}+1$

Set Theory Proof Practice Problem Help [CONFUSED]

Prove that every measurable set $E \subset \mathbb{R}$ is the union of a Borel set and a set of measure 0(2)

equipollent couple of points to define vectors

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