Question

Prove that $\mathbb{Z}\times\mathbb{N}$ is not isomorphic to $\mathbb{Z}\times\mathbb{Z}$ (both strictly ordered): is my proof correct?

score 1.6k · Answer 1 · 2026-04-10 16:07:22

1.6k

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Prove that $\mathbb{Z}\times\mathbb{N}$ is not isomorphic to $\mathbb{Z}\times\mathbb{Z}$ (both strictly ordered): is my proof correct?

Published on 10 Apr 2026 - 16:07

score 108 · Answer 2 · 2026-04-12 21:27:53

108

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Cardinality of a space of continuous functions

Published on 12 Apr 2026 - 21:27

score 2.9k · Answer 3 · 2026-04-12 07:26:12

2.9k

Views

How can a finite set not have a maximum or minimum?

Published on 12 Apr 2026 - 7:26

score 487 · Answer 4 · 2018-03-22 19:43:53

487

Views

Proving that the set of all functions from $\mathbb{N}$ to $\{4, 5, 6\}$ is uncountable

Published on 22 Mar 2018 - 19:43

score 1k · Answer 5 · 2026-03-29 15:43:51

1k

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Proving the set of real numbers is uncountable

Published on 29 Mar 2026 - 15:43

score 58 · Answer 6 · 2026-03-25 17:39:21

58

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Assune A,B,C,D are sets such that $|A |= |B |$ and $|C |= |D |$. Show that $|C^A |= |D^B |$

Published on 25 Mar 2026 - 17:39

score 2.5k · Answer 7 · 2026-04-12 06:26:15

How does the Cantor's diagonal argument that $(0,1)$ is uncountable deals with the fact some real numbers have two different decimal expansions?

score 56 · Answer 8 · 2026-03-27 02:35:23

56

Views

Can we write it as $A$ is closed under the action of $T$?

Published on 27 Mar 2026 - 2:35

score 226 · Answer 9 · 2026-04-09 00:25:45

226

Views

Is this composition associative?

Published on 09 Apr 2026 - 0:25

score 84 · Answer 10 · 2018-03-23 18:58:57

84

Views

How can I show that this function is injective, surjective or bijective?

Published on 23 Mar 2018 - 18:58

score 44 · Answer 11 · 2026-04-12 13:34:02

44

Views

Set and Inequality, something like generating function.

Published on 12 Apr 2026 - 13:34

score 61 · Answer 12 · 2026-04-12 14:47:30

61

Views

Methods for finding some function $h$ with the property that, given two functions $f,g$, then $h\circ f=g\circ h$ is true?

Published on 12 Apr 2026 - 14:47

score 135 · Answer 13 · 2026-04-13 03:21:23

135

Views

Prove the transitiveness of the asymmetric part of the transitive relation. Using a set language.

Published on 13 Apr 2026 - 3:21

score 81 · Answer 14 · 2018-03-24 15:10:48

81

Views

Can every natural number $8m - 3$ be written as either $o_c(n,x)$ or $o_d(n,x)$?

Published on 24 Mar 2018 - 15:10

score 1.1k · Answer 15 · 2026-04-12 03:31:55

1.1k

Views

Finite union of countable sets is countable.

Published on 12 Apr 2026 - 3:31

List Question

Prove that $\mathbb{Z}\times\mathbb{N}$ is not isomorphic to $\mathbb{Z}\times\mathbb{Z}$ (both strictly ordered): is my proof correct?

Cardinality of a space of continuous functions

How can a finite set not have a maximum or minimum?

Proving that the set of all functions from $\mathbb{N}$ to $\{4, 5, 6\}$ is uncountable

Proving the set of real numbers is uncountable

Assune A,B,C,D are sets such that $|A |= |B |$ and $|C |= |D |$. Show that $|C^A |= |D^B |$

How does the Cantor's diagonal argument that $(0,1)$ is uncountable deals with the fact some real numbers have two different decimal expansions?

Can we write it as $A$ is closed under the action of $T$?

Is this composition associative?

How can I show that this function is injective, surjective or bijective?

Set and Inequality, something like generating function.

Methods for finding some function $h$ with the property that, given two functions $f,g$, then $h\circ f=g\circ h$ is true?

Prove the transitiveness of the asymmetric part of the transitive relation. Using a set language.

Can every natural number $8m - 3$ be written as either $o_c(n,x)$ or $o_d(n,x)$?

Finite union of countable sets is countable.

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