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Contemporary Math: Help and Review9 chapters | 119 lessons

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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.

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.

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.

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.

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.

This unique symbol is used with sets but not with lines. For intersecting lines, there is no symbol that is used.

The point or points at which two things meet is called their intersection. Two lines can have one point of intersection, no intersection, or an infinite number of points of intersection. The intersection of sets involves finding the items that the sets have in common. If the sets have nothing in common, then they don't have an intersection. If all the sets have a common item or items, then the collection of those common items is the intersection of those sets.

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13 in chapter 9 of the course:

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Contemporary Math: Help and Review9 chapters | 119 lessons

- Introduction to Graph Theory 4:34
- Graph Theory Concepts and Terminology 8:08
- Euler Paths and Euler's Circuits 6:11
- Mathematical Models of Euler's Circuits & Euler's Paths 6:54
- Euler's Theorems: Circuit, Path & Sum of Degrees 4:44
- Fleury's Algorithm for Finding an Euler Circuit 5:20
- Eulerizing Graphs in Math 5:57
- Hamilton Circuits and Hamilton Paths 3:26
- Assessing Weighted & Complete Graphs for Hamilton Circuits 5:06
- The Traveling Salesman Problem in Computation 4:46
- Methods of Finding the Most Efficient Circuit 8:17
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