Set Definition

A set is a group of objects called the elements of the set. Mathematics uses sets composed of numbers as their elements for evaluating equations. A mathematical set must be well defined. A set can contain an infinite number of elements, as long as it not ambiguous in definition. For example, the set of all real numbers is a well-defined set that is infinite. This set is sometimes designated with a capital R. The empty set is the one set with no elements. Comparing the set of all real numbers which includes all the fractions to the set of all natural numbers (sometimes designated with a capital N) shows the first infinite set is larger than the second infinite set. One way of comparing infinite sets is by showing a one to one correspondence between each of the set's elements. All levels of math from basic mathematics up to geometry, trigonometry and beyond use sets to evaluate functions. The domain set is the defined group of numbers that the equation will evaluate. When defining a domain the Greek letter epsilon is sometimes used to represent the term "elements of" in the definition. If the domain is undefined it is usually assumed be the set of all real numbers. The answer set to a function is its range.

In the mathematical equation x + 1, x plus one, the elements of both the domain set and range set are all real numbers.

In the mathematical equation x + 1 for x greater than five, the domain is defined as the set of all real numbers greater than five, the range is all real numbers greater than six.

In the mathematical equation (0 x x) + 1, zero times x plus one, the domain set is all real numbers and the range set is just the number one, because in this equation for any value x the solution is the number one, because zero times any number is always equal to zero.