User:Guy vandegrift/sandbox/BLANK

Universe
Naive set theory is a way of talking about sets (collections of objects) using plain language, without the strict rules of formal logic. A good example of the success of naive set theory is counting the number of possible sets, given the proposition that the "universe" consists of sets that are only allowed to contain three letters: x, y, and z. Even this "universe" allows us to create the eight different sets shown in the figure.


 * Russell's paradox


 * Peano axioms


 * Surreal number

Place "0" on the number line. Nothing is to the left and noting is to the right:

Day 0: Φ < "0" < Φ

Going from left to right, place entities on each side of "0"

Day 1: Φ < a < "0" < A < Φ

Now place entities around each of these three:

Day 2: Φ < b < a < c < "0" < C < A < B < Φ

Place A to the right of Φ, and a to the left of Φ.