$(10$ pts$)$ A binary string is any sequence of zeros and ones. Let $A$ be the set of binary strings having only $1\text{'}$s$.$ In other words, $A=\{1,11,111,1111,$dots$\}.$ Prove by contradiction that $A$ is of infinite size. That is$,$ prove by contradiction: $P$:$ninN,|A|=n.$

$(10$ pts$)$ Prove by induction: P: AAninN,EEminN,$n^3+2n=3m$