List questions from natural-numbers

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List Question

All combinations for $x_i+y_j$ in a finite sets of real numbers

proof $\forall n \exists p (p^2 \leq n <(p+1)^2)$

Multiplication Law for Order on Integers

Existence of closures of sets

Example of a bijection from $\mathbb{N}$ to $\mathbb{N}$x$\mathbb{N}$

What is a definitive explanation for the following property of natural numbers?

What $x \in IN$ mean?

Solving equation of two variables, solution in natural numbers

Presentability of natural numbers (number theory)

Is there a power of $2$ whose last digit is a $0$?

How to prove there are no natural numbers between 0 and 1?

Well-ordering principle: why it is needed to state, and then make use?

Statement of Well-ordering principle

Goldbach-like and Collatz-like conjectures and theorems

$X$ is infinite thus we have an injection from $\mathbb{N}$ to X

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