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Sets

In modern mathematics, just about everything rests on the very important concept of the set.

A set is just a collection of elements, or members. For instance, you could have a set of friends:

F = {Abdul, Gretchen, Hubert, Jabari, Xiomara}

or a set of numbers:

Y = {–3.4, 12, 9999}

You can also have infinitely large sets:

Z = the set of all integers = {..., –3, –2, –1, 0, 1, 2, 3, ...}

M = {x | x > 3}

(This last notation means "all real numbers x such that x is greater than 3." So, for example, 3.1 is in the set M, but 2 is not. The vertical bar | means "such that".)

You can also have a set which has no elements at all. This special set is called the empty set, and we write it with the special symbol .

If x is a element of a set A, we write , and if x is not an element of A we write .

So, using the sets defined above,

, since –862 is an integer, and

, since 2.9 is not greater than 3.

See also subsets and operations on sets.