Item.

If we want to prove that a statement is true for all values of \(n\) (greater than some first small value), and we can describe why the statement being true for \(n = k\) implies the statement is true for \(n = k+1\text{,}\) then the principle of mathematical induction gives us that the statement is true for all values of \(n\) (greater than the base case).

in-context