Question

Peano axioms vs set construction of natural numbers

score 442 · Answer 1 · 2021-10-02 12:12:21

442

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Peano axioms vs set construction of natural numbers

Published on 02 Oct 2021 - 12:12

score 102 · Answer 2 · 2021-10-03 13:32:46

102

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Why is the principle of induction for natural numbers not "self-evident"?

Published on 03 Oct 2021 - 13:32

score 63 · Answer 3 · 2021-10-03 17:47:31

63

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Is the theory of sequence convergence requiered by limits?

Published on 03 Oct 2021 - 17:47

score 201 · Answer 4 · 2021-10-04 00:44:16

201

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Are odd natural numbers an inductive set?

Published on 04 Oct 2021 - 0:44

score 166 · Answer 5 · 2021-10-06 05:58:42

166

Views

Why bijection between $\mathbb{N^2}$ and $\mathbb{N}$ is not possible directly?

Published on 06 Oct 2021 - 5:58

score 106 · Answer 6 · 2021-10-06 21:00:36

106

Views

Why Cantor diagonalization theorem is failed to prove $S$ is countable, Where $S$ is set of finite subset of $\mathbb{N}$?

Published on 06 Oct 2021 - 21:00

score 101 · Answer 7 · 2026-03-26 01:03:13

101

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Directly proof $S$ is countable, where $S$ is set of function from $\{0, 1\}$ to $\mathbb{N}$

Published on 26 Mar 2026 - 1:03

score 72 · Answer 8 · 2021-10-12 18:42:02

72

Views

Uniqueness of finite measures that agree on $\mathcal{H} \subset \mathbb{N}$

Published on 12 Oct 2021 - 18:42

score 143 · Answer 9 · 2026-03-26 17:53:23

143

Views

$H(n)=\lfloor\dfrac{b}{n}\rfloor- \lfloor \dfrac{a}{n} \rfloor=$ (roughly) # odd pairs $o, o+2 \in [a,b]$ such that $n \mid o$ or $n \mid o+2$

Published on 26 Mar 2026 - 17:53

score 456 · Answer 10 · 2021-10-19 19:19:24

456

Views

What formula of ZFC defines the set of natural numbers?

Published on 19 Oct 2021 - 19:19

score 139 · Answer 11 · 2021-10-20 06:59:00

139

Views

Formula for the number of pairs of odd numbers $x, x+2k \subset [a,b]$ such that $n \mid x$ or $n \mid x + 2k$? Previous solution was $k = 1$ only.

Published on 20 Oct 2021 - 6:59

score 252 · Answer 12 · 2026-03-29 19:11:02

252

Views

Can the natural numbers contain an element that is not representable by a number?

Published on 29 Mar 2026 - 19:11

score 55 · Answer 13 · 2026-03-29 19:09:30

55

Views

Finiteness, finite sets and representing its elements.

Published on 29 Mar 2026 - 19:09

score 258 · Answer 14 · 2026-03-29 19:14:29

258

Views

How to prove that there are $n$ natural numbers that are less or equal than $n$ and what properties are allowed to use in induction.

Published on 29 Mar 2026 - 19:14

score 982 · Answer 15 · 2021-11-09 09:59:42

982

Views

The set of Fibonacci numbers formalized in set-theoretic notation: did I do it correctly?

Published on 09 Nov 2021 - 9:59

List Question

Peano axioms vs set construction of natural numbers

Why is the principle of induction for natural numbers not "self-evident"?

Is the theory of sequence convergence requiered by limits?

Are odd natural numbers an inductive set?

Why bijection between $\mathbb{N^2}$ and $\mathbb{N}$ is not possible directly?

Why Cantor diagonalization theorem is failed to prove $S$ is countable, Where $S$ is set of finite subset of $\mathbb{N}$?

Directly proof $S$ is countable, where $S$ is set of function from $\{0, 1\}$ to $\mathbb{N}$

Uniqueness of finite measures that agree on $\mathcal{H} \subset \mathbb{N}$

$H(n)=\lfloor\dfrac{b}{n}\rfloor- \lfloor \dfrac{a}{n} \rfloor=$ (roughly) # odd pairs $o, o+2 \in [a,b]$ such that $n \mid o$ or $n \mid o+2$

What formula of ZFC defines the set of natural numbers?

Formula for the number of pairs of odd numbers $x, x+2k \subset [a,b]$ such that $n \mid x$ or $n \mid x + 2k$? Previous solution was $k = 1$ only.

Can the natural numbers contain an element that is not representable by a number?

Finiteness, finite sets and representing its elements.

How to prove that there are $n$ natural numbers that are less or equal than $n$ and what properties are allowed to use in induction.

The set of Fibonacci numbers formalized in set-theoretic notation: did I do it correctly?

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