# Difference between revisions of "Set"

A set is a collection of objects. Sets are the subject of set theory. Two sets are the same if they contain the same elements, regardless of the order they are in. Sets are written in set notation, such as {1,2} indicating the set containing the elements 1 and 2. This is the same as the set {2, 1} because order does not matter when comparing sets.

Also, repetition of elements is irrelevant, so the set {1, 2, 2} is the same as the set {1, 2}.

An important concept in set theory is cardinality. In the case of finite sets, this is simply the number of elements of the set. So {1, 2} has a cardinality of 2. However, the theory is more complicated in the case of infinite sets.

It was thought that an informal concept of sets (Naive set theory) was sufficient, however Russell's Paradox shows that this can lead to a contradiction if sets are allowed to contain themselves. Modern set theory is more formal, and disallows such paradoxical sets.

## Application

There is the set of unborn children who were aborted, about which striking conclusions can be drawn. Given the large and diverse number of elements of this set, it would likely include many who could surpass existing athletic and intellectual achievements. Indeed, many of the world records and Nobel Prize achievements recognized today would have been outdone by members of this set.

Another striking example is the how traditional marriage provides a greater set than otherwise: the union of A = {a, b, c, d} and B = {a, b, c, e} is merely {a, b, c, d, e}, while the union of M (man) = {a, b, c, d} and W (woman) = {e, f, g, h} is {a, b, c, d, e, f, g, h}, which is a broader and more diverse set.