Prove √2 exists by Archimedean Axiom
6582
Prove the existence of the square root of $2$.
49750
Proof of the square root inequality $2\sqrt{n+1}-2\sqrt{n}<\frac{1}{\sqrt{n}}<2\sqrt{n}-2\sqrt{n-1}$
67605
Different proof that $\sqrt{2}$ is irrational
56818
Prove that if $A$ is positive, then $\exists\;\alpha>0$ such that $\langle Ax, x \rangle\geq \alpha|x|^2$ for $x\in\Bbb{R}^n$
125164
How to prove the existence of $b$ in $Q$ such that $a<b^2<c$ in $Q$?
126632
Proving Inequalities with Absolute values
68275
Primitive Root Theorem Proof
80920
Prove or disprove: For any $v\in\mathbb{R}^n, \|v\|_1\|v\|_\infty \leq \frac{1+\sqrt{n}}{2}\|v\|_2^2$
138632
Proof that if $a > 0$, then $\frac{1}{a} > 0$ using just field and order axioms
141529
Proving existence of a minimum
107765
Prove that there exists two roots in $[-1,1]$
142000
Prove that there is an irrational number and a rational number between any two distinct real numbers
20161
Prove that the multiplicative inverse of $a$ modulo $m$ exists if and only if $a$ and $m$ are coprime.
23752
Proving Irrationality
63409
If $x^2+ax+b=0$ has a rational root, show that it is in fact an integer
139979
Proof there is a rational between any two reals
77026
Proof with inequalities