prove that $|\{0,1\}^{\mathbb{N}}|\leq |\mathbb{R}|$
41052
The set of real numbers and power set of the natural numbers
51347
Prove that $|a|\leq \max\{|b|,|c|\}$ if $b\leq a \leq c$
55752
Prove that $n+1$ vectors in $\mathbb{R}^n$ cannot be linearly independent
28125
Showing that $1 - \frac{x^2}2\leq\cos x$, $\forall x \in \mathbb{R}$
40930
Prove that $ex \leq e^x$ for all $x \in \mathbb{R}$
95293
Proof that $|\sqrt{x}-\sqrt{y}| \leq \sqrt{|x-y|},\quad x,y \geq 0$
149056
Prove that for all $n\geqslant 1$ we have $F_n<{\left(\frac 74\right)}^n$.
46039
Prove that if $x \in R,$ then there exists $n \in Z$ satisfying $x \leq n < x+1$
118049
Show that $\mathbb{R}^{\mathbb{R}} = U_{e} \oplus U_{o}$
103536
How to prove $|e^{i\theta} - 1| \leq |\theta|$?
80009
Prove that $| |a|-|b| | \le |a-b|$
66441
Prove that $|x|<1$ implies that $\lim_{n \to \infty} x^n=0$
149287
Prove that $A,B>0$ and $A_{ij}0$
140409
Prove that $\sqrt{n} > \ln n$
33673
Proving $N(x) = (A(x,x))^\frac12$ is a norm in $V$ given that A is a positive definite bilinear form
126821
Let $f:[0,1]\to \mathbb{R}$. Show that $\{a \in [0,1]: f(a)\neq 0\} = \bigcup_{n=1}^{\infty} \{a \in [0,1]: |f(a)|\geq 1/n\}$
133228
Prove $(|x| + |y|)^p \le |x|^p + |y|^p$ for $x,y \in \mathbb R$ and $p \in (0,1]$.