Discover published sets by community

Show that the statement holds for the first natural number, usually 0 or 1.

Prove the statement for the base cases, which may include several initial natural numbers, not just the first.

A detailed verification that the base case meets the condition of the theorem or statement being proved.

State that, since the basis step and inductive step have been proved, by induction the statement is true for all natural numbers.

The assumption that the statement holds for some arbitrary case $k$.

Arriving at the end of the induction process, concluding the statement holds for all natural numbers.

Assume the statement holds for all natural numbers less than $k$ and show it holds for $k$.

Show that each case follows from the previous one, or from the collection of all previous ones in strong induction.

Assume the statement holds for some arbitrary natural number $k$ and show it holds for $k+1$.