How to show that every nonempty $X \subset \mathbb N$ has an $\in$-minimal element
91281
Proving the so-called "Well Ordering Principle"
59724
Proving that $x_n\to L$ implies $|x_n|\to |L|$, and what about the converse?
37183
Show that the set of all $x$ such that $x \in P$ and $x \notin Q$ exists
88598
Property of $\{0^n, 1^n, \ldots\}$
119180
How to prove that the set $A = \left\{ {p:{p^2} < 2,p \in {\Bbb Q^+}} \right\}$ has no greatest element?
103744
Minimal $ab$ for Rational Number $a/b$ in an Interval
104855
Prove that $N \subset Z(G)$
14713
$X=(-\infty,0]\cup\left\{{1\over n}:n\in\mathbb N\right\}$ with subspace topology Then
116943
Proof for maximal ideals in $\mathbb{Z}[x]$
11817
Proving that every set $A \subset \Bbb N$ of size $n$ contains a subset $B \subset A$ with $n | \sum_{b \in B} b$
75039
Smallest positive element of $ \{ax + by: x,y \in \mathbb{Z}\}$ is $\gcd(a,b)$
45405
An elementary way to show any bounded subset of $\Bbb{R}^k$ is totally bounded
157218
If $E\subseteq X$ is connected, $E\cap A\neq\emptyset$ and $E\cap(X\setminus A)\neq\emptyset$ then $E\cap\partial A\neq\emptyset$
144745
Proof of: If $x_0\in \mathbb R^n$ is a point of local minimum of $f$, then $\nabla f(x_0) = 0$.
51687
Is the set $ \ (\mathbb{Z}_p \setminus \mathbb{Z}) \cap \mathbb{Q}$ non-empty?
33157
Proof that an infinite subset of $\mathbb{N}$ is countable
113582
How can I find an element $x\not\in\mathfrak mM_{\mathfrak m}$ for every maximal ideal $\mathfrak m$