Induction

Question 1

What is mathematical induction?

Answer 1

A proof technique which exploits the conctruction of the set of natural numbers. In its basic formula it says:

Question 2

What it basic recursion?

Answer 2

Definining something in terms of itself. In terms of its use in mathematical structures, it usually means using a function in its own definition:

Question 3

Can variations on induction and recursion have different or multiple base cases?

Answer 3

Yes

Question 4

What is strong induction?

Answer 4

A refined form of basic induction in which:

• the base step works the same
• for the inductive step, we prove the the statement of a generic natural k+1 holds if we assume that the statement holds for any natural greater than or equal to k

Question 5

Need to do practice on these