### Articles/Mathematics/Other/Set Theory

A set is essentially a group of objects. These objects can have some kind of common feature, or they can be entirely unrelated. For example, assume set A={dog, 1, 8823, hamster, automobile, Jim, (555) 555-5555}. The objects in this set do not seem to have any overall common feature, although some of the individual items share common features with other items. A set can also be defined by the category of its contents by way of set B={all words in the english language}. In this case, all of the objects aren't listed since it would be incredibly long. However, by looking at the definition, one is able to understand what objects would be contained within the set.

Each object in a set is called an element. A set containing elements in common with the elements in another set is said to be a subset. For example, assume set A={1,2} and set B={1,2,3,4,5}. In this case the set A is a subset of set B since all of the objects in set A are also found in set B. Set B is clearly not a subset of set A. Assume another set C={1,2}. Although A and C are equivalent sets, it can be said that A is a subset of C and vice versa.

The intersection between two sets is the elements that are contained in both sets. For example, assume set A={hamster, monkey, elephant} and set B={dog, cat, elephant, zebra, dolphin, monkey}. The intersection of sets A and B produce the resultant set {elephant, monkey}.

The union between two sets is a combination of all unique elements contained in both sets. Using the previously defined sets, the intersection of sets A and B would produce the set {dog, cat, elephant, monkey, zebra, dolphin, hamster}.