# What does [0,1] X [0,1) mean?

## Homework Statement

Determine whether the following in R^2 are compact or not.

(i) [0,1] X [0,1)
(ii) [a,b] X [c,d] where a < b, c < d

## The Attempt at a Solution

I have seen this notation before but I never knew what it meant.

## Answers and Replies

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LeonhardEuler
Gold Member
It means a rectangle. For instance if you call R^2 the x-y plane, then [0,1] X [0,1) would be the set of numbers where
$$0\leq x \leq 1$$
and
$$0\leq y < 1$$

gb7nash
Homework Helper
Draw a square in R2 space with vertices at (0,0),(0,1),(1,0) and (1,1) and shade the box. The side edges and bottom edge are closed and the top edge is dotted. So any point on the top edge is not in the region [0,1] X [0,1).

Euler beat me. :(