List questions from natural-numbers

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What is the definition of a positive integer?

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Random Algebra Problem 2

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Why is the sum over all positive integers equal to -1/12?

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If $\frac1\alpha+\frac1\beta=1$, irrational, then $\{\lfloor n\alpha\rfloor:n\in\Bbb N\}\uplus\{\lfloor n\beta\rfloor:n\in\Bbb N\}=\Bbb N$

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List Question

Is $\lim\limits_{n \to \infty} n$ "equal" to $\mathbb{N}$?

Random Algebra Problem

What is the definition of a positive integer?

Random Algebra Problem 2

Why is the sum over all positive integers equal to -1/12?

If $\frac1\alpha+\frac1\beta=1$, irrational, then $\{\lfloor n\alpha\rfloor:n\in\Bbb N\}\uplus\{\lfloor n\beta\rfloor:n\in\Bbb N\}=\Bbb N$

$3^a\mid s(n) \Rightarrow 3^a\mid n$

Biggest 8 digit number following two specific rules

Notation regarding the maximum function over a list of naturals

Prove the commutativity property of addition of natural numbers by induction

Proving an inequality for all natural numbers involving parameters

Number of unique products of two integers of bounded size

Sum of sum of $k$th power of first $n$ natural numbers.

proof of commutativity of multiplication for natural numbers using Peano's axiom

Zero divided by zero

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