How to make segments Hello can anyone help me to understand how to describe segments on the Cartesian plane using Cartesian products.
Like for example, how can I interpret 
$$(-\infty,-1) \times (-\infty,-1)$$
and
$$(0,1) \times (-\infty,1)$$
How could this be expanded for example/ what is it really saying?
I am only used to the product with the basic examples, such as when you have individual elements in a set A and a set B.
Thank you to anyone for help.
 A: For the second set, $(0,1)$ means $0<x<1$ since its first in the product. So graph dotted vertical lines $x=0,x=1$ and remember you're shading between these. The lines are dotted to indicate boundary points not in set. Then your second factor $(-\infty,1)$ means just $y<1,$ so plot the horizontal line $y=1$ (again dotted since it's $<$ not $\le$) This time you'll shade below that line. Put the two together (or consider where both shadings occur).
A: You get all the points $(x,y)$ where $$-\infty < x < -1$$                       & $$-\infty < y < -1$$ Basically, an "infinite" rectangle (red) with its upper right corner at $(-1,-1)$ (which itself is not included, since you have two open sets). 

Analogously for the second example (blue): This time you have
$$0 < x < 1$$
$$-\infty < y < -1$$
being a rectangle which is $1$ unit broad (upper edge between $(0,-1)$ and $(1,-1)$) and starts stretching infinitely downwards after $y=-1$. Again, its edges are not included since you have round brackets instead of squared ones.
