Cartesian Product of two sets?

  • #1

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
 

Answers and Replies

  • #2
329
34
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.
 
  • #4
329
34
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.
 
  • #5
34,687
6,393
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.
 
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