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What Is a Set?
A set is a clearly defined collection of distinct objects, called its elements.
Defining a Set
Curly brackets { } show a set. Each thing inside is called an element or member of the set. Order does not matter, and nothing is listed twice.
A set must be "well-defined": anyone should be able to say for certain whether something belongs or not. "The set of tall people" is not a proper set, because "tall" means different things to different people. "The set of people over cm" is a proper set.
Example 1 — a simple set
Let A be the set of the first four odd numbers.
- The first four odd numbers are , , , .
- Write the set: A = {, , , }
Answer: A = {, , , }
Example 2 — checking membership
Let B = {, , , }. Is a member of B?
- Look through every element of B: , , , .
- does not appear in the list.
- So is not a member of B. We write ∉ B.
Answer: No, ∉ B
The symbol ∈ means "is a member of". The symbol ∉ means "is not a member of". For B = {, , , }: ∈ B, but ∉ B.
Practice
More lessons in Sets and Functions · Next: Describing Sets · Previous: Introduction