Show that $x_{\alpha} \rightarrow x$ in $M$ iff $x_{\alpha}$ is eventually equal to x.
96074
A net $\varphi : [0, \omega_1) \to M$ on a metric space $M$ converges $\iff \varphi$ is eventually constant
155579
Show that $End_A(A)$ = {$r_a$ | $a ∈ A$}
102598
Show that $X$ is path connected if and only if each $X_\alpha$ is path connected.
38242
Explicit bijection between the successor of $\alpha$ and $\alpha$ (infinite ordinal).
24785
How prove this equation $\alpha=\aleph_{0}\alpha$
56878
Proof that $a\mid b \land b\mid c \Rightarrow a\mid c $
106585
Show $d_{1}(x_{n},x)\rightarrow{0}$ if and only if $d_{2}(x_{n},x)\rightarrow{0}$.
59724
Proving that $x_n\to L$ implies $|x_n|\to |L|$, and what about the converse?
8913
Show that there is $\xi$ s.t. $f(\xi)=f\left(\xi+\frac{1}{n}\right)$
21881
Prove that $\forall\alpha\geq\omega$, $|L_\alpha|=|\alpha|$ without AC
108012
A matrix $M$ that commutes with any matrix is of the form $M=\alpha I$
83291
Prove that $p(x)=(x-a)q(x)$ for some $q(x)\in R[x]$ of degree= (degree of $p)-1$.
43219
If $[K(\alpha):K]=p\neq q=[K(\beta):K]$ then $[K(\alpha+\beta):K]=pq$
150385
The use of the Axiom of Choice in this proof of the sequence lemma
113534
Show that any metrizable space $X$ is Hausdorff
24466
Prove that if $[F(\alpha):F]$ is odd then $F(\alpha)=F(\alpha^2)$
80939
How to show that every $\alpha$-Hölder function, with $\alpha>1$, is constant?