Lecture 2 - Mathematical Induction

Question 1

What are the steps (by name) in a mathematical induction proof?

Answer 1

1. Basis step

2. Induction Step

Question 2

What happens in the basis step?

Answer 2

Attempt to prove that S(1) is true

Question 3

What happens in the induction step?

Answer 3

1. Assume that S(n) is true for n greater than or equal to 1

2. Prove that S(n+1) is true by inserting S(n+1) on both sides of the equation

Question 4

if |X| = n, then what is |P[X]|? (If cardinality of X is n, what is cardinality of Powerset of X?)

Answer 4

2^n for all n

Question 5

What is the sum of the first n positive integers?

Answer 5

n(n+2) / 2