Venn Diagrams and Set Theory

I was researching Set Theory last night, and after thinking a little bit, I realized that geometric numbers could be used to represent items in a set. I was trying to figure out if you could make a Venn-type diagram to represent all of the subsets as equal areas. I figured out 4 sets...

but I couldn't find out what the pattern was until later. Let's say you are making a Venn-type diagram out of X sets. There would have to be all possible intersections included, or 2^X different areas. So, if 2^X is any kind of geometric number, then it can be constructed from that (regular?) geometric shape. Just a little theory...

Set theory is like the coolest thing ever. It's like all of logic in one tiny part of math. It's important for probability, exponents, and number theory, of other things. It's the idea that we can group everything, rearrange, them, and still  have the same thing. How cool is that?

The most basic functions of sets are complements (what isn't in a set), unions (the combination of sets), intersections (what two sets have in common), and if (or if and only if) statements. Combining functions and sets, you can separate out any part.


That's pretty cool.

STay coolio,
John