List questions from natural-numbers

Published on 14 Apr 2026 - 17:37

53

Views

Why does $Pair(x,y) = \frac{(x+y)(x+y+1)}{2} + x$ exhibit a bijection with the pairs (x,y)?

Published on 16 Apr 2026 - 3:02

52

Views

Existence of $T$ such that $[(T\circ T)(f)](n)=f(n+1)$

Published on 16 Apr 2026 - 16:19

2.7k

Views

Proving $n \leq 3^{n/3}$ for $n \geq 0$ via the Well-Ordering Principle

Published on 14 Apr 2026 - 8:07

103

Views

Are the natural numbers definable in the (2nd-order) theory of complete ordered fields?

Published on 13 Apr 2026 - 12:59

2.1k

Views

Natural numbers as a subset of integer numbers: $\mathbb{N}\subset\mathbb{Z}$.

Published on 12 Apr 2026 - 5:59

62

Views

Complicated index models and Boolean algebras/ Shelah/ Unclear step in the proof

Published on 07 Apr 2026 - 3:12

939

Views

Product $\sigma$-algebra of power sets

Published on 15 Apr 2026 - 1:26

165

Views

$a < b$ and $c<d$ imply $a+c < b+d$

Published on 11 May 2026 - 6:36

55

Views

$a = d$ implies $a^b = d^b$

Published on 15 Apr 2026 - 23:17

53

Views

$1 < a$ and $b\ne0$ imply $1<a^b$

Published on 16 Apr 2026 - 14:17

4.6k

Views

Are there any two numbers such that multiplying them together is the same as putting their digits next to each other?

Published on 13 Apr 2026 - 21:24

53

Views

Help proving there is a sequence of rational numbers

Published on 12 Apr 2026 - 16:17

49

Views

Definition of the Number Two in ZF Set Theory

Published on 13 Apr 2026 - 11:03

95

Views

On randomly permuting digits in a large random number

Published on 15 Apr 2026 - 13:23

List Question

Prove using induction that $n^6 < 3^n$,for all $n > 18$

Why does $Pair(x,y) = \frac{(x+y)(x+y+1)}{2} + x$ exhibit a bijection with the pairs (x,y)?

Existence of $T$ such that $[(T\circ T)(f)](n)=f(n+1)$

Proving $n \leq 3^{n/3}$ for $n \geq 0$ via the Well-Ordering Principle

Are the natural numbers definable in the (2nd-order) theory of complete ordered fields?

Natural numbers as a subset of integer numbers: $\mathbb{N}\subset\mathbb{Z}$.

Complicated index models and Boolean algebras/ Shelah/ Unclear step in the proof

Product $\sigma$-algebra of power sets

$a < b$ and $c<d$ imply $a+c < b+d$

$a = d$ implies $a^b = d^b$

$1 < a$ and $b\ne0$ imply $1<a^b$

Are there any two numbers such that multiplying them together is the same as putting their digits next to each other?

Help proving there is a sequence of rational numbers

Definition of the Number Two in ZF Set Theory

On randomly permuting digits in a large random number

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