MAT 25 Lecture Notes - Lecture 8: Qnh, Open Set, Empty Set
Document Summary
{x} -> a set is closed if its complement is open: real numbers: for nay x within r, n(x)cr for any epsilon>0 => r is open. R contains all its limit points => r is closed. Empty set is closed since r^c =empty and open since r is closed: half open intervals. [0,1) not open because of the closed zero but it also is not closed because 1 is a limit point of the set that allows the set to have infinite numbers that approaches 1 yet does not reach 1. Q (rational numbers) are neither closed nor open. Because the irrationals are also dense q in q, r in q-epsilon, q+epsilon) for same r within i => q is not open square root (2) is not within q.
