Introduction to Real Analysis 1 Prove that the least upper b

Introduction to Real Analysis

1. Prove that the least upper bound of [0,1) is 1

Solution

If A = [0, 1)then 1 is a least upper bound for A. Indeed, 1 is an upper
bound for A, and if x < 1 then x cannot be an upper bound for A (because then either
x < 0 (so x is not an upper bound because 0 A), or 0 x < 1 in which case x A
and 1 > x, so x is not an upper bound).