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 70,000 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

- Inclusion in Recruitment, Interviews & Hiring
- Computer Science 105: Introduction to Operating Systems
- High School 101: High School Readiness
- Communications 301: Diversity and Intercultural Communication
- Communications 106: Communication in the Digital Age
- Operating System Fundamentals
- Cultural Differences in Nonverbal Communication
- Techniques for Inclusive Hiring & Onboarding
- Intro to Inclusion in Recruitment, Interviews & Hiring
- Implementing Inclusion in Recruitment & Screening
- CLEP Prep Product Comparison
- CLEP Exam vs. AP Test: Difficulty & Differences
- CLEP Tests for the Military
- How to Transfer CLEP Credits
- CLEP Exam Question Formats
- CLEP Exam Costs & Registration Deadlines
- CLEP Exam List & Credits Offered

- Static vs. Non-Static Methods in Java
- South African Flag Lesson for Kids: Colors & Meaning
- Monkey Facts: Lesson for Kids
- Peter Senge: Learning Organizations & Systems Thinking
- Students with Dual-Sensory Impairment: Characteristics & Accommodations
- Pharmaceutical Compounding: Equipment & Supplies
- How Physiology of the Brain Affects Emotional Intelligence
- Risk Reporting: Communication & Techniques
- Quiz & Worksheet - The Crucible & Symbols
- Quiz & Worksheet - Various Perspectives on Organizations
- Animal Adaptations: Quiz & Worksheet for Kids
- Quiz & Worksheet - Serving Alcohol Responsibly
- Quiz & Worksheet - Email Message Anatomy
- How to Cite Sources Flashcards
- Evaluating Sources for Research Flashcards

- History 107: World Conflicts Since 1900
- Middle School Physical Science: Tutoring Solution
- Financial Accounting: Homework Help Resource
- CLEP Principles of Macroeconomics: Study Guide & Test Prep
- High School Chemistry Textbook
- ScienceFusion Ecology & the Environment Unit 1.2: Roles in Energy Transfer
- NES Phys Ed: Movement Concepts & Biomechanics
- Quiz & Worksheet - Adding Integers
- Quiz & Worksheet - Sources of Population Data
- Quiz & Worksheet - Relationship Between Molecule Function & Shape
- Quiz & Worksheet - Measuring Viscosity
- Quiz & Worksheet - Montgomery Bus Boycott

- Active & Passive Transport in Cells
- Yellowstone National Park Volcano: Facts & History
- Best Place to Study Abroad
- Of Mice and Men Lesson Plan
- Congress of Vienna Lesson Plan
- Memorial Day History Facts
- Good Persuasive Writing Topics for Middle School
- Conjunctions Lesson Plan
- Chicago Adult Education
- Fiction Writing Prompts
- Five Themes of Geography Lesson Plan
- Short Story Lesson Plan

Browse by subject