We need the standard definition of finite and infinite.

Definition $0\mathrm{.}2.$ A set $S$ is finite if there exists an integer $n$ such that $|S|=n.$ A set is infinite if it

is not finite.

Consider the language

$L=\{w|win\{a,b{\}}^{**},w$ has less $a\text{'}s$ than $b\text{'}s\}.$

Prove that $L$ is infinite if it is infinite, or finite if it is finite.