# Intersection in Math: Definition & Symbol

Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

In this lesson, you will learn about how intersection works in math for both lines and sets. Also, learn how you can easily communicate intersection to others by using a unique symbol.

## Definition

An intersection is the meeting point of two things.

What do you picture when you hear the word intersection? For me, I picture two roads meeting together at a stop light. You know how one road goes one way and the other road goes the other way? That is what I picture. They meet or cross each other at the intersection.

In math, the intersection of two things is the same. When two things come together, their intersection is the point or points at which they cross.

## Intersection of Lines

Let's look at how it works with lines. When you have two lines in math that intersect each other, you will have a point or points at which they meet.

This meeting of the lines is what we call the intersection of two lines. We can have several different scenarios when it comes to the intersection of lines. Let's go through them one by one.

1. Two different lines that are not parallel to each other will only have one point of intersection. If the lines are different and are not parallel, they will eventually cross each other. They will only cross each other once at exactly one point. When the lines are graphed on the coordinate plane, you can specify the point by giving the coordinate of the point of intersection.

2. Two different lines that are parallel will never intersect and will not have a point of intersection. Think about that. What does it mean to be parallel? It means that the two lines will never meet, correct? Yes, and if that is the case, they will never intersect.

3. Two lines that are the same are parallel to each other and intersect at all points on the line. Two lines that are the same essentially lie on top of each other and share all the same points. We can say that their intersection is the line itself. In this case, there is more than one point of intersection. The two lines actually have an infinite number of intersection points because lines go on forever.

## Intersection of Sets

There is another area in math where you have intersection and that is when dealing with sets or groups of items. A set in math is a group of items. It can be a group of numbers, variables, or anything else you can think of. When two or more groups have an item or items in common, the subset of items they have in common is what we call the intersection of sets.

For example, let's say we had two different sets of numbers. Set A has the numbers {2, 4, 6, 8} and Set B has {6, 8, 10, 12}. Do these two sets have anything in common? Yes, they do. Both sets have a 6 and an 8. So, the intersection of Set A and Set B is {6, 8} because those items are what they have in common.

## Intersection Symbol for Sets

For the intersection of sets, we do have a special symbol. This symbol looks like an upside down U, as shown in this example problem.

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