If we have an assertion \(S_i\) for an integer \(i\) that is known to be true for \(i\) equal to \(k\) and can show that if \(S_i\) is true then \(S_{i+1}\) must also be true then we can be sure that \(S_i\) is true for all \(i\) greater than or equal to \(k\), known as proof by induction.