EECS 376 Lecture Notes - Lecture 1: Natural Number, Contraposition, Additive Inverse

• School: U of M
• Department: Electrical Engineering And Computer Science
• Course: EECS 376
• Professor: Martin Strauss

Document Summary

Think of modulus as returning the remainder after division. a = b(mod n) i a b is divisible by n: zn is the set of integers de ned modulo n. All the possible remainders if n is divided by any value: contains n elements, namely, 0, 1, , n 1. 0 is equivalent to all integer multiples of kn. 1 is equivalent to kn + 1 for all integer values of k. In z2, there are two elements, 0 and 1. 1. 2 operations in zn: all operations are done modulo n in zn. In z4, 2 + 3 = 5 = 1. In z4, 3 3 = 9 = 1. The inverse of x in zn is simply n x. In z5, the additive inverse of 2 is just 3 because 2 + 3 = 5 = 0(mod 5): multiplicative inverse x x 1 = 1(mod n).