Prove: If $(a_n)\to\infty$, then $(1/a_n)\to0$
As $a_n\to\infty$, for every $C>0$ there exists an $N$ in the natural numbers such that we have
$a_n>C$ whenever $n>N$
$\implies|a_n|>C$ whenever $n>N$
$\implies|1/a_n| < 1/C$ whenever $n>N$
If follows that if we choose $e>0$ there exists an $N_1$ such that we have
$|1/a_n| < e$ whenever $n>N_1$
How is this proof, is it acceptable do you think?