deathmtn

Zermelo developed nine simple axioms, that is, unproven basic assumptions, on which everything is based in math.
These are still used today. One of the axioms is: “There is an empty set.” …And, in fact, this is the only set that Zermelo constructed so explicitly. The other rules say, for example, that you can “combine two sets to form a third set” or “select an element from a set.”

Everything else follows from the empty set, the “zero.” For example, the numbers are constructed from it. To do this, it helps to imagine a set as a bag into which you can pack objects. An empty set corresponds to an empty bag.

When constructing the numbers, Zermelo started with zero. It corresponds to the empty set or empty bag. “One” is the quantity into which the previously defined zero is packed, so it’s a bag with an empty bag inside. Two is the quantity that contains the 1 and the 0, or a bag containing a bag that itself contains a bag.