List questions from natural-numbers

Published on 13 Oct 2013 - 17:56

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sequence of sets with $\limsup A_n = \mathbb N$

Published on 14 Oct 2013 - 20:52

83

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For any $a \in \mathbb R$ and any $n \in \mathbb N^+$ there exists $q \in \mathbb Q$ such that $|a-q|< \frac{1}{n}$.

Published on 14 Oct 2013 - 22:51

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Proving $mn = 0$ implies $m = 0$ or $n=0$ for all $m, n \in \mathbb{N}$ using Peano Axioms

Published on 28 Mar 2026 - 10:04

111

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How to prove $\frac{1}{m+n+1}-\frac{1}{(m+1)(n+1)} ≤ \frac{4}{45}$?

Published on 21 Oct 2013 - 4:08

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Peano system vs natural numbers

Published on 28 Mar 2026 - 10:04

5.3k

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how many different numbers are there with 3 digits and that add up to 19?

Published on 25 Oct 2013 - 21:53

1.3k

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About the Collatz conjecture

Published on 29 Mar 2026 - 4:42

84

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$5^a - 5^b$ is divisible by $n$ (prove)

Published on 03 Nov 2013 - 16:51

58

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ZF Natural Even Numbers

Published on 13 Nov 2013 - 13:37

15.5k

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How to divide by 12 quickly?

Published on 13 Nov 2013 - 16:28

941

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An example of a total order (that is NOT a well-order) of the Natural numbers

Published on 14 Nov 2013 - 20:44

120

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Prove that one of $2^n +1$ and $2^n-1$ must be composite for $n$ is a natural number greater than $2$

Published on 14 Nov 2013 - 22:52

138

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Counting how many natural numbers satisfy a given condition.

Published on 17 Nov 2013 - 15:54

480

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Help needed with an equivalence relation task on natural numbers

Published on 18 Nov 2013 - 17:36

List Question

Induction on natural numbers

sequence of sets with $\limsup A_n = \mathbb N$

For any $a \in \mathbb R$ and any $n \in \mathbb N^+$ there exists $q \in \mathbb Q$ such that $|a-q|< \frac{1}{n}$.

Proving $mn = 0$ implies $m = 0$ or $n=0$ for all $m, n \in \mathbb{N}$ using Peano Axioms

How to prove $\frac{1}{m+n+1}-\frac{1}{(m+1)(n+1)} ≤ \frac{4}{45}$?

Peano system vs natural numbers

how many different numbers are there with 3 digits and that add up to 19?

About the Collatz conjecture

$5^a - 5^b$ is divisible by $n$ (prove)

ZF Natural Even Numbers

How to divide by 12 quickly?

An example of a total order (that is NOT a well-order) of the Natural numbers

Prove that one of $2^n +1$ and $2^n-1$ must be composite for $n$ is a natural number greater than $2$

Counting how many natural numbers satisfy a given condition.

Help needed with an equivalence relation task on natural numbers

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