Class Notes (839,194)
Canada (511,223)
CSCB36H3 (2)

Day 1 Sep 12

3 Pages

Computer Science
Course Code
Nick Cheng

This preview shows page 1. Sign up to view the full 3 pages of the document.
CSCB36 Nick Cheng Chapter 1: Natural Numbers: ℕ = { 0, 1, 2, … } Predicates on Natural Numbers: P 1n): ∑n=0n = n(n+2) / 2 P (n): there are n students in B36 2 Let P be a predicate on ℕ. Principle of Simple Induction (PSI): Suppose P(0) holds, For all n ≥ 0, [P(n) => P(n+1)] Suppose also for any n ≥ 0, if P(n) holds, then P(n+1) holds. Then we can conclude: P(n) holds for all n ≥ 0. P(0), P(0) => P(1), P(1) => P(2), … Principle of Complete Induction (PCI): Suppose P(0) holds, Suppose for any n > 0, if P(j) holds whenever 0 ≤ j < n, then P(n) Then we can conclude: P(n) holds for all n ≥ 0. P(0), P(0) => P(1), P(0) and P(1) => P(2), P(0) + (P(1) + P(2) => P(3), … Principle of Well Ordering (PWO): Suppose A ⊆ ℕ and A ≠ ∅ Then we can conclude: A has a minimum element i.e a # m s.t m ≤ m’ for all m’ ∈ A Proofs: e.g 1.7: Stamps: P(n): n cents of postage can be made using only 4c & 7c stamps. n = K * 4 + L *
More Less
Unlock Document

Only page 1 are available for preview. Some parts have been intentionally blurred.

Unlock Document
You're Reading a Preview

Unlock to view full version

Unlock Document

Log In


Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Sign up

Join to view


By registering, I agree to the Terms and Privacy Policies
Already have an account?
Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.

Add your courses

Get notes from the top students in your class.