Prove that $|\mathbb R^n | = |\mathbb R|$.
14322
Examples of bijective map from $\mathbb{R}^3\rightarrow \mathbb{R}$
124562
$f:\mathbb{R}^n \to \mathbb{R}$ has expansion $\sum_i g_i(x)x^i$
151803
Prove that $R$ is commutative
80827
Let $A$ be a nonempty subset of $\mathbb{R}$. Prove...
37569
Prove that $\binom{n}{r} + \binom{n}{r+1} = \binom{n+1}{r+1} $
102817
$A,B\in M_{n}(\mathbb{R})$ so that $A>0, B>0$, prove that $\det (A+B)>\max (\det(A), \det(B))$
15733
Show that the cardinality of $\mathbb N$ is the same as the cardinality of $\mathbb N \times \mathbb N$
63183
Suppose $a,b,m,n$ are natural numbers, prove that if $a({m \over n})=b$ and $(a,n)=1$, then ${m \over n} \in \mathbb{N}$
21737
If $A|B$ and $B|A$ then prove $A=\pm B$
39114
Prove that a set in $\mathbb R^3$ is not an algebraic set
100375
Prove that ${\sqrt {n} }^{\sqrt {n+1}} > {\sqrt {n+1}}^{\sqrt {n}}$.
125868
Prove $a \equiv b \pmod{c} \implies a^n \equiv b^n \pmod{c}$.
92740
prove that $\mathbb{Q}^n$is dense subset of $\mathbb{R^n}$
149382
Prove that $(0,1) \subseteq\mathbb R$ and $(4,10) \subseteq\mathbb R$ have the same cardinality.
77957
How is $\mathbb N$ actually defined?
106584
If $A^{2n}=I$, then $A^n=\pm I$ where $A\in M_n(\mathbb{R})$
2575
Showing that $\mathbb{R}$ is connected