List questions from proof-writing

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Why are these two segments of the same length?

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Prove for all natural numbers $n ≥ 2: n! <\big( \frac{n + 1}{2}\big)^n$

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Elementary Number Theory Proof Modulo

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List Question

Simple proof for take-and-flip-over game solution

How to show the equivalence of two hyperplane representations?

Derive formula for the area of triangle provided that you know 2 angles and side between them.

Proof by induction - stuck on simple question!

Tiling a square problem

Why are these two segments of the same length?

How would you prove an equality of sums of set cardinalities?

Prove for all natural numbers $n ≥ 2: n! <\big( \frac{n + 1}{2}\big)^n$

I was asked to prove the Principle of Cauchy Induction

Real Analysis Proof with absolute values

Proving the contrapositive statements

Prove that for a convergent sequence $(a_n)$ of real numbers $ inf(a_n) \le \lim_{n\to \infty} a_n = a \le sup(a_n)$ (not by contradiction)

Elementary Number Theory Proof Modulo

Proving Euler's product formula for sine

Prove Supremum and Infimum

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