Homework Statement
Does [0,1] \times [0,1] in the dictionary order have the least upper bound property?Homework Equations
Dictionary Order. (on \mathbb{R}^2) Let x , y \in \mathbb{R}^2 such that x=(x_1 , x_2) and y = (y_1 , y_2). We say that x < y if x_1 < y_1, or if x_1 = y_1 and x_2 < y_2...