Question

Show that every positive even integer is of the form $2n$ and every positive odd integer is of the form $2n+1$.

Answer 1

By the definition of even number, every even number is divisble by $2$.
$E=2n$ where $n\in N$.
By the definition of odd number, every odd number is not divisble by $2$. The only possible remainder when divided with $2$ is $1$.

Hence odd numbers can be of the form $2n+1$ where $n$ is the quotient when divided with $2$.
$O=2n+1$ where $n\in W$