Theorem 3.4.1 : Principle of Mathematical Induction
If S⊆N such that
1∈S , and
k∈S⇒k+1∈S ,
then S=N .
Step-by-step explanation:
Definition: Mathematical Induction
To show that a propositional function P(n) is true for all integers n≥1 , follow these steps:
Basis Step: Verify that P(1) is true.
Inductive Step: Show that if P(k) is true for some integer k≥1 , then P(k+1) is also true.
