EECS 1019 Study Guide - Midterm Guide: Negative Number, Mathematical Induction, Cardinality

• School: York University
• Department: Electrical Engineering and Computer Science
• Course: EECS 1019
• Professor: Suprakash Datta

Document Summary

Nov 21, 2011: (15 points) cardinality: determine which of these sets is countably in nite, or uncountable. For those that are countably in nite, exhibit a one-to-one correspondence between the set of positive integers and that set. (a) (5 points) the odd negative integers. Solution: this set (call it s1) is countably in nite. The set of positive integers is also the set of natural numbers n. the correspondence is f : n s1, f(n) = (2n 1). (b) (5 points) the integers that are multiples of 7. Solution: this set (call it s2) contains both positive and negative integers. So let us use 0 to map to 0, the even numbers to map to the positive numbers and the odd numbers to map to the negative number. Solution: in this case we have to dispense with the positive integers rst, before dealing with the negative ones. Solution: for the base case we use n = 5.