# Cartesian Product of two sets?

## Homework Statement

I need to answer a bunch of topological questions based on the cartesian product of two sets, but I'm not entirely sure how to graph them out.

I have A = [1,2)U{3} and B = {1, (1/2), (1/3), ...}U[-2,-1). S = A x B, and I need the graph of S.

Could anyone help me with this?

## The Attempt at a Solution

This is my original "sketch" but I'm almost positive it is wrong. http://i.imgur.com/NqOSnkh.jpg

Set up the interval [1,2) and the 3 along the x-axis. In a sense A is a set with 1 element -- a strange element but just one.

Set up the interval [-2,-1) along the y-axis.

I think each element of A X B will be those two intervals, plus the point (3,1/n). If that makes sense, it is easy enough to graph.

I'm sure you are closing in on this and you may be right. I am not sure. I am far from expert at this kind of thing, so you probably need a more reliable opinion.

You might look thru your class notes to see if anything similar was mentioned. Or perhaps one of the mentors would look this over.

Mark44
Mentor
Would it be like this? I think I've got it.

http://i.imgur.com/TxF7bae.jpg
Yes, that's it. The box you have in the 2nd quadrant threw me off for a bit, but I see that this is not actually part of your graph.

Some fine points that your graph doesn't show:

The horizontal lines in the 1st quadrant get closer and closer together as the y values get closer to 0.
The points that you show in the 1st quadrant do the same thing.

Your graph shows (correctly) that the rectangular region in Q IV includes the left and bottom edges, but does not include the top and right edges.

Your graph also shows (correctly) that the vertical line segment in Q IV includes the lowest point, but not the highest one.

1 person