Number Sets (ℕ, ℤ, ℚ, ℝ): Belonging to Sets
Learn what it means for an element to belong to a set. Practice the ∈ and ∉ symbols with concrete, visual exercises.
Belonging to Sets
Solved: 0
A set A is shown below. Does the highlighted element belong to A (∈) or not (∉)?
Learning Topics
What is a Set? Belonging (∈) and Not Belonging (∉)
A set is simply a collection of distinct objects — called elements or members. We write a set by listing its elements inside curly braces, like
We use two special symbols to describe membership:
• ∈ (belongs to / is an element of): We write
• ∉ (does not belong to): We write
Key idea: To check membership, just look at the list! If the element appears inside the curly braces, it belongs (∈). If it doesn't appear, it does not belong (∉).
Example: For
•
•
A = {2, 5, 8, 11}.We use two special symbols to describe membership:
• ∈ (belongs to / is an element of): We write
5 ∈ A to say "5 is in set A". Since 5 is listed inside A above, this is true.• ∉ (does not belong to): We write
7 ∉ A to say "7 is not in set A". Since 7 is not listed, this is true.Key idea: To check membership, just look at the list! If the element appears inside the curly braces, it belongs (∈). If it doesn't appear, it does not belong (∉).
Example: For
B = {1, 3, 5, 7, 9}:•
3 ∈ B ✓ (3 is in the list)•
4 ∉ B ✓ (4 is not in the list)Learning Topics
Frequently Asked Questions
What is a set and what are its elements?
A set is a collection of distinct objects or numbers called elements. We write a set by listing its elements inside curly braces, like A = {1, 2, 3}.
What do the symbols ∈ and ∉ mean?
The symbol ∈ means “belongs to” or “is an element of” (e.g. 2 ∈ {1, 2, 3} is true). The symbol ∉ means “does not belong to” (e.g. 4 ∉ {1, 2, 3} is true).