ECE103 Study Guide - Midterm Guide: Haplogroup R1B, Verb

• School: University of Waterloo
• Department: Electrical and Computer Engineering
• Course: ECE103
• Professor: Martin Pei

Document Summary

Definition 2. 1. 1 we say that the integer a divides the integer b, and write that a|b, if there is an integer q such that b = qa. If a does not divide b, we write a |b. From the definition for divisibility, one can deduce the well known fact that 0 |n for any nonzero integer n. Proof: if 0|n, then there is an integer k such that 0k = n. but 0k = 0, so 0 = n, contradicting the fact that n = 0. Note that this holds even if n = 0; that is, 0|0. Proposition 1: let a, b, c be integers. (i) if a|b and b|c, then a|c. (ii) if a|b and b|a, then a = b. (iii) if a and b are positive integers such that a|b, then a b. Proof. (i) since a|b and b|c, by definition there are integers p and q such that b = pa and c = qb.