Discrete mathematicsLesson 1 of 2 in the course Set theory and relations

Set Theory: Notation, Operations, Functions, and Infinite Sets

5 flashcards · 5 quiz questions · 5 match pairs · 4 fill-in sentences · English

Save course
Lesson progress
0 / 5

Your progress is kept in this browser only.Sign up to save it

Summary

This lesson introduces sets, their elements, and the basic notation used to describe them. Sets provide a common language for organizing mathematical objects and form a foundation for modern mathematics.

A set is a collection of distinct objects, called its elements or members. Elements may be numbers, symbols, geometric objects, functions, or even other sets. The statement that xx is an element of SS is written x∈Sx ∈ S. If yy is not an element of SS, write y∉Sy ∉ S.

All flashcards

What is a set?
A collection of distinct objects, called its elements or members.
What do ∈∈ and ∉∉ mean?
x∈Sx ∈ S means xx belongs to SS; x∉Sx ∉ S means it does not belong to SS.
What is the empty set?
The unique set with no elements, denoted ∅∅ or {}.
What is the difference between ∅∅ and ∅{∅}?
∅∅ has no elements. ∅{∅} has one element, namely the empty set.
How does set-builder notation work?
It specifies a set by a property, as in x∣P(x){x \mid P(x)}, meaning all xx for which P(x)P(x) is true.

Quiz questions

  1. What does the notation x∈Sx ∈ S state?Answer: It says that xx belongs to SS.
  2. How many elements does the empty set contain?Answer: Zero elements.
  3. Why are {∅}\{∅\} and ∅∅ different sets?Answer: One contains ∅∅ as an element; the other has no elements.
  4. What does the vertical bar mean in x∣P(x){x \mid P(x)}?Answer: It means “such that.”
  5. Which statement about {1,2,3}\{1,2,3\} and {3,1,2,2}\{3,1,2,2\} is correct?Answer: They contain the same elements.

Based on the Wikipedia article Set (mathematics), licensed CC BY-SA 4.0. Adapted into a summary, flashcards and quizzes.

More in Discrete mathematics

All Discrete mathematics lessons
Discrete mathematicsBinary Relations: Operations, Properties, Functions, and Applications5 flashcards · 5 quiz questions · 4 gamesPlay free →Discrete mathematicsPigeonhole Principle: Counting, Collisions, and Applications5 flashcards · 5 quiz questions · 4 gamesPlay free →Discrete mathematicsDe Morgan's Laws in Logic, Set Theory, and Boolean Algebra5 flashcards · 5 quiz questions · 4 gamesPlay free →Discrete mathematicsEulerian Routes: Criteria, Construction, and Extensions5 flashcards · 5 quiz questions · 4 gamesPlay free →Discrete mathematicsNumber Theory: Integer Structure, Methods, and Applications5 flashcards · 5 quiz questions · 4 gamesPlay free →Discrete mathematicsBinomial Coefficients: Expansion, Counting, and Identities5 flashcards · 5 quiz questions · 4 gamesPlay free →