For $0 \to N' \to N \to M \to 0 $ with $N$ finitely generated and $M$ finitely presented then $N^{'}$ is also finitely generated.
109080
Is the kernel of a map to a finitely presented module finitely generated?
19599
$ d(x_n,y_n) \to d(x,y)$ if $x_n\to x$ and $y_n \to y$
98017
If $a_{n+1}/a_n\to\ell$ show $a_n^{1/n}\to\ell$
103732
Proving that for $n \equiv 0 \pmod{2}$, we get ${n \choose 0} < {n \choose 1} <\ldots< {n \choose n/2-1}<{n\choose n/2}$ etc.
95244
Prove that a finite union of closed sets is also closed
8360
$\sum_i x_i^n = 0$ for all $n$ implies $x_i = 0$
157847
If $x_n \to 0$, show that $\sqrt{x_n} \to 0$
154796
Completeness of sequence of reals with finitely many nonzero terms
75373
Show that $2^n>n$ for $n\in \mathbb{N}$
75970
$\mathbb Z[1/2]$ is not finitely generated?
81
$\lim_{n\to \infty}f(nx)=0$ implies $\lim_{x\to \infty}f(x)=0$
108429
Show that if $x_n \to x$ then $\sqrt{x_n} \to \sqrt{x}$
69515
If $x_n\cdot y_n\to 0$ then $x_n \to 0$ or $y_n \to 0 $
152223
If $0<r<1$ show that $r^n$ goes to $0$ as $n$ goes to 1.
148413
Proving $S_n$ is generated by the set $\{(1\text{ }2),(2\text{ }3),\cdots,(n-1\text{ }n)\}$ of $n-1$ transpositions.
46971
Number of surjections from $\{1,...,m\}$ to $\{1,...,n\}$
77735
When $\Bbb Z_n$ is a domain. Counterexample to $ab \equiv 0 \Rightarrow a\equiv 0$ or $b\equiv 0\pmod n$