Question

How do mathematicians know if they are extending the theory of natural numbers in the right direction?

score 396 · Answer 1 · 2026-03-26 19:01:48

396

Views

How do mathematicians know if they are extending the theory of natural numbers in the right direction?

Published on 26 Mar 2026 - 19:01

score 75 · Answer 2 · 2023-04-12 15:07:51

75

Views

how many linear orderings on $\omega$ the are and how can we identify when 2 of them are in fact isomorphic.

Published on 12 Apr 2023 - 15:07

score 175 · Answer 3 · 2026-03-26 19:18:38

175

Views

Is the set of all linear orders on $\mathbb{N}$ linearly orderable?

Published on 26 Mar 2026 - 19:18

score 494 · Answer 4 · 2026-03-27 05:59:42

494

Views

How do Peano's axioms make it clear what the successor is equal to?

Published on 27 Mar 2026 - 5:59

score 165 · Answer 5 · 2023-04-14 13:30:35

165

Views

Why set of natural numbers with its customary ordering by magnitude is not a totally ordered set?

Published on 14 Apr 2023 - 13:30

score 357 · Answer 6 · 2023-04-23 10:44:46

357

Views

True or false: For every $N\in\mathbb{N}$, there exists $k\in\mathbb{N}$ such that $\sin{(k^n)}<0$ for $n=1,2,3,...,N$.

Published on 23 Apr 2023 - 10:44

score 54 · Answer 7 · 2023-04-30 14:57:15

54

Views

Given the inequalities $n > 2^k - 1$ and $n < 2^{(k+1)}$, express $k$ in terms of $n$ (where $k, n \in\Bbb N$).

Published on 30 Apr 2023 - 14:57

score 107 · Answer 8 · 2023-05-01 02:25:18

107

Views

Order relations on natural number objects in topoi, and symmetry

Published on 01 May 2023 - 2:25

score 139 · Answer 9 · 2023-05-10 08:00:23

139

Views

A dominance issue in two ordered sequences of integers

Published on 10 May 2023 - 8:00

score 45 · Answer 10 · 2026-02-23 00:50:45

45

Views

Upper and lower hemicontinuity of correspondences defined on natural numbers

Published on 23 Feb 2026 - 0:50

score 45 · Answer 11 · 2023-05-20 23:44:32

45

Views

proving properties of $\Bbb N$ after constructing it as a subset of $\Bbb R$

Published on 20 May 2023 - 23:44

score 86 · Answer 12 · 2023-06-01 18:51:02

86

Views

Explicit enumerations of n-tuples of naturals $f:\mathbb{N}^n \to \mathbb{N}$?

Published on 01 Jun 2023 - 18:51

score 16 · Answer 13 · 2023-06-04 11:46:03

16

Views

Prove commutative of entanglement of two natural numbers.

Published on 04 Jun 2023 - 11:46

score 101 · Answer 14 · 2023-06-06 11:57:59

101

Views

How to find the sum of all the five-digit numbers that can be made using $0, 0, 1, 2, 3, 4$

Published on 06 Jun 2023 - 11:57

score 201 · Answer 15 · 2023-06-11 17:02:13

201

Views

Asymptotic sum of set of natural numbers with positive natural density

Published on 11 Jun 2023 - 17:02

List Question

How do mathematicians know if they are extending the theory of natural numbers in the right direction?

how many linear orderings on $\omega$ the are and how can we identify when 2 of them are in fact isomorphic.

Is the set of all linear orders on $\mathbb{N}$ linearly orderable?

How do Peano's axioms make it clear what the successor is equal to?

Why set of natural numbers with its customary ordering by magnitude is not a totally ordered set?

True or false: For every $N\in\mathbb{N}$, there exists $k\in\mathbb{N}$ such that $\sin{(k^n)}<0$ for $n=1,2,3,...,N$.

Given the inequalities $n > 2^k - 1$ and $n < 2^{(k+1)}$, express $k$ in terms of $n$ (where $k, n \in\Bbb N$).

Order relations on natural number objects in topoi, and symmetry

A dominance issue in two ordered sequences of integers

Upper and lower hemicontinuity of correspondences defined on natural numbers

proving properties of $\Bbb N$ after constructing it as a subset of $\Bbb R$

Explicit enumerations of n-tuples of naturals $f:\mathbb{N}^n \to \mathbb{N}$?

Prove commutative of entanglement of two natural numbers.

How to find the sum of all the five-digit numbers that can be made using $0, 0, 1, 2, 3, 4$

Asymptotic sum of set of natural numbers with positive natural density

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