Back To Course

Math 102: College Mathematics15 chapters | 121 lessons | 13 flashcard sets

Watch short & fun videos
**Start Your Free Trial Today**

Start Your Free Trial To Continue Watching

As a member, you'll also get unlimited access to over 55,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Free 5-day trial
Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Kathryn Maloney*

Kathryn teaches college math. She holds a master's degree in Learning and Technology.

In this video, we will add to our knowledge of sets. We will talk about cardinality, infinite, finite, equal and the empty set. I think you will find these very straightforward, so let's begin.

Before we be begin to talk about cardinality and types of subsets, let's review sets. A **set** is a collection of elements. An **element** is a collection of anything - numbers, letters, words, or objects. Using math symbols, this means element:

The number of elements in a set is called the **cardinality** of the set. The cardinality of set *V* = {car, truck, van, semi} is four. There are four elements in set *V*.

There are two ways I have seen the symbol for cardinality. The first has straight bars, like the absolute value symbol. In symbols, |*V*| = 4. The cardinality of set *V* is 4. The second way I've seen it written is with an *n* and then the set in parenthesis. In symbols, *n*(*V*) = 4. The cardinality of set *V* is 4.

An **empty set** is one that is, well, empty. It doesn't have any elements. Let's say set *E* is an empty set. We can write set *E* in symbols like this:

The cardinality of set *E* is 0. We would write it as |*E*| = 0. Be warned, zero is not an element in the set; it simply means the set has no elements!

Let's look at the set of primary colors: *P* = {red, yellow, blue}. We can say that set *P* is a **finite set** because it has a finite number of elements. Finite means we can count the number of elements. In this case, set *P* has 3 elements: red, yellow, and blue. Set *P* has a cardinality of 3 because there are 3 elements in the set. We would write it as |*P*|= 3.

An **infinite set** is a set with an infinite number of elements. There are two types of infinite sets - countable and uncountable. A *countable infinite set* is one that can be counted in one sitting, though you may never get to the last number. An example of a countable infinite set is the set of all integers. An *uncountable infinite set* is one that cannot be counted because it is too large. An example of an uncountable infinite set is the set of all real numbers. The set of all real numbers equals all rational numbers and irrational numbers.

**Equal sets** are those that have the exact same elements in both. Let's say set *A* = {red, blue, orange} and set *B* = {orange, red, blue}. Then, set *A*= set *B*. We can say set *A* = set *B* because they have the same elements - red, blue, orange - even though they are not in order.

**Equivalent sets** are those that have the same cardinality, or number of elements. Let's say set *Q* is {red, blue, orange} and set *R* is {3, 4, 6}. We can say set *Q* is equivalent to set *R* because they both have a cardinality of 3. They both have 3 elements. Equivalent doesn't mean they have to be the same elements.

**Cardinality** of a set is the number of elements in that set. It can be written like this:

An **empty set** is one that doesn't have any elements. An empty set can be written like this:

A **finite set** has a countable finite number of elements.

An **infinite set** is a set with an infinite number of elements. There are two types of infinite sets: countable and uncountable.

**Equal Sets** are those that have the exact same elements in both.

**Equivalent Sets** are those that have the same cardinality.

Upon reaching the end of this lesson, you could be able to:

- Recognize cardinality, empty set, equal sets and equivalent sets
- Contrast finite and infinite sets and provide examples of each
- Create cardinality and empty sets using math symbols

To unlock this lesson you must be a Study.com Member.

Create
your account

Already a member? Log In

BackDid you know… We have over 95 college courses that prepare you to earn credit by exam that is accepted by over 2,000 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
2 in chapter 12 of the course:

Back To Course

Math 102: College Mathematics15 chapters | 121 lessons | 13 flashcard sets

- Go to Logic

- Mathematical Sets: Elements, Intersections & Unions 3:02
- Cardinality & Types of Subsets (Infinite, Finite, Equal, Empty) 4:13
- Venn Diagrams: Subset, Disjoint, Overlap, Intersection & Union 6:01
- Categorical Propositions: Subject, Predicate, Equivalent & Infinite Sets 4:24
- How to Change Categorical Propositions to Standard Form 3:28
- What is a Two-Way Table? 3:40
- Go to Sets

- Go to Geometry

- FTCE ESOL K-12 (047): Practice & Study Guide
- GACE Media Specialist Test II: Practice & Study Guide
- GACE Media Specialist Test I: Practice & Study Guide
- GACE Political Science Test II: Practice & Study Guide
- NES Essential Components of Elementary Reading Instruction: Test Practice & Study Guide
- 20th Century Spanish Literature
- Sun, Moon & Stars Lesson Plans
- Direct Action & Desegregation from 1960-1963
- Civil Rights Movement from the Civil War to the 1920s
- Civil Rights in the New Deal & World War II Era
- Common Core State Standards in Ohio
- Resources for Assessing Export Risks
- Preview Personal Finance
- California School Emergency Planning & Safety Resources
- Popsicle Stick Bridge Lesson Plan
- California Code of Regulations for Schools
- WV Next Generation Standards for Math

- The Chorus in Antigone
- Where is Mount Everest Located? - Lesson for Kids
- Sperm Cell Facts: Lesson for Kids
- The Motivational Cycle: Definition, Stages & Examples
- Bolivian President Evo Morales: Biography & Quotes
- Labor Unions for Physicians: Benefits & Factors
- Positive Attitude & Call Center Performance
- Chicken Facts: Lesson for Kids
- Quiz & Worksheet - Converting English Measurement Units
- Quiz & Worksheet - What Is Felony Murder?
- Quiz & Worksheet - Characteristics of Agile Companies
- Quiz & Worksheet - A Bend in the River
- Quiz & Worksheet - Sentence Fluency
- Growth & Opportunity for Entrepreneurs Flashcards
- Understanding Customers as a New Business Flashcards

- AP US History Syllabus Resource & Lesson Plans
- Accuplacer ESL Language Use Test: Practice & Study Guide
- 12th Grade English Textbook
- Human Growth & Development Syllabus Resource & Lesson Plans
- SAT Biology: Help and Review
- The Cardiovascular System
- The Atmosphere: Homework Help
- Quiz & Worksheet - Non-Sterile Glove Procedures
- Quiz & Worksheet - Forces that Affect Trade in Global Markets
- Quiz & Worksheet - Organizing and Understanding Data with Tables & Schedules
- Quiz & Worksheet - Romantic Era Composers
- Quiz & Worksheet - Sacred vs. Secular Renaissance Music

- Sensory Coding: Getting Messages from Receptors to Your Brain
- English Monarchs: History & Timeline
- GRE Scores Percentile Information
- Figurative Language Lesson Plan
- Expository Writing Prompts
- Best MCAT Prep Books
- Communism Lesson Plan
- How is the GED Scored?
- When Do PSAT Scores Come Out?
- Shays' Rebellion Lesson Plan
- Federalism Lesson Plan
- GRE Exam Registration Information

Browse by subject