Sets, Relations, and Functions

A set is a collection of numbers or other mathematical objects, without repetitions. Any set of points in a table or on a graph is called a relation. Some relations are functions. In this lesson you will learn the difference between relations and functions. You will also learn about the domain and range of relations and functions.


Sets

A set is a collection of numbers or other mathematical objects, each of which occurs only once. We write sets using curly braces. For example, {2,3,4} is the set which contains the numbers 2, 3, and 4.

Question 1 of 7. What is the largest number in the set {2,3,4}?

You can list a set’s elements in any order. For example, {1,3,5} and {5,1,3} are the same set.

What is the smallest number in the set {5,1,3}?

Sometimes, instead of listing everything contained in a set, we want to give some condition that the numbers in the set have to satisfy. For example, we might want to talk about the set of all positive numbers (numbers greater than zero). The notation for this is {x:x>0}, which you should read as “the set of all x such that x is greater than 0” or “the set of all x which are greater than 0.”

Is the number 3 in the set {x:x>0}?
Is the number 2 in the set {x:x3}?
Is the number 5 in the set {x:2x7}? (2x7 means 2x and x7 are both true.)
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