Solution
= Solution
{c}
A <sequence> $(a_n)$ of <real numbers> is a <convergent sequence> with <limit of a sequence> $\ell$ when
$$
\boxed{\forall\varepsilon>0\ \exists N\in\mathbb N\ \forall n\geq N:\quad |a_n-\ell|<\varepsilon.}
$$
Divergence to positive <infinity> means
$$
\boxed{\forall M\in\mathbb R\ \exists N\in\mathbb N\ \forall n\geq N:\quad a_n>M.}
$$
In both definitions the same $N$ must control every later term. The second condition is not convergence to a <real number>.