
A set is a collection of unique objects. A set can't contain two identical (indistinguishable) objects. Consider the set of rational numbers, which are numbers that can be expressed as a/b, where a is an integer and b is a nonzero integer. This set contains 2/4, and this set contains 4/8, because they can both be expressed as a/b. But these are not two different elements of the set. 2/4 and 4/8 are two different ways of expressing the same element. This means, for one thing, that if D is the set of all rationals except 2/4, then D does not contain 4/8.
A list of elements, separated by commas, enclosed in curly braces.
Example: {3, 5, 7} is the set of singledigit odd prime numbers.
Tricky Example: { { }, {3}, {5}, {7}, {3,5}, {3,7}, {5,7}, {3,5,7} } is the set of subsets of the set of singledigit odd prime numbers. Notice that every element of this set is itself a set. The roster notation allows the use of nested curlybraces to describe sets which have other sets as elements.
Infinite set in roster notation: {1, 2, 3, ...} is the set of positive integers. The first few elements illustrate the pattern, and the ellipsis (three dots) indicate that the pattern continues indefinitely.
Setbuilder notation is a shorthand way of saying "the set of all numbers, x, such that x has this property..."
Example: {a/b : a is an integer, b is a nonzero integer} is the set of rational numbers.
The colon means "such that". Sometimes a vertical bar is used instead of a colon.
An "interval" is a connected subset of the real number line. Each end of an interval can be "open" or "closed". An "open" end does not include its endpoint, and a "closed" end does.
Examples:
(2,3) means {x : x > 2 and x < 3}
[2,3) means {x : x ³ 2 and x < 3}
(2,3] means {x : x > 2 and x £ 3}
[2,3] means {x : x ³ 2 and x £ 3}[2,∞) means {x : x ³ 2}
(∞,3) means {x : x < 3}
Notice that if one end goes on to infinity (or negative infinity), this end must be an open end. This is because infinity is not, itself, a real number, so it can't be included in any subset of real numbers.
A number line, representing the set of real numbers, is a thin line with an arrow at both ends. The set of all numbers greater than a, where a is a real number, is represented by a darker line with a hollow point at a, and dark arrow to indicate that the set continues forever:
The set of all numbers greater than or equal to a is represented by a ray with a solid endpoint:
The set of numbers less than a is
The set of numbers less than or equal to a is
The set of numbers greater than or equal to a, and less then b is
Sets  how to construct sets of integers, reals, etc.
Functions  an introduction to the concept of a function, using setbuilder notation to describe the "domain" and "range" of a function.
Box and whisker plot  a way to graphically characterize a set of numbers.
The webmaster and author of this Math Help site is Graeme McRae.