EECS 1019 Study Guide - Final Guide: Loop Invariant, Bijection, Rational Number

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

Document Summary

Instructor: s. datta: (2 points) evaluate the in nite geometric series. Note that the left hand side is 0. 99 . Use the answer above to ll in the blank below. Solution: this is a geometric series with a = 0. 9 and r = 0. 1. 1 0. 1 = 1: (2 points) express the following statement in predicate logic: given any 2 distinct rational numbers, there exists a rational number between them in value . Solution: make the domain q, the set of rational numbers. X y[(x (cid:54)= y) ( z(x < z < y) (x > z > y))]: (2 points) prove that if f : z+ z, f (n) = n2 100n then f (n) (n2). Solution: note that n2 100n n2/2 if n 200. So we use n0 = 200, c = 0. 5 in the de nition of (n2) and thus f (n) (n2): (2 points) what is the negation of x yp (x) q(y).