Proof by Induction (Leaving Cert Mathematics): Flashcards

A technique to prove statements true for all natural numbers or specified integers

Natural numbers ($n \in \mathbb{N}$) or subset of integers

Sequences, inequalities, or formulas

3 steps

Verify statement is true for initial value of $n$

Assume $P(k)$ is true for some $k \ge n_0$

The assumption that $P(k)$ is true for some $k \ge n_0$

Use inductive hypothesis to prove $P(k+1)$ is true

The inductive hypothesis