🦭 Number Sets (ℕ, ℤ, ℚ, ℝ)
Learn what it means for an element to belong to a set. Practice the ∈ and ∉ symbols with concrete, visual exercises.
Belonging to Sets
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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
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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, which are called elements or members. We write a set by listing its elements inside curly braces, like A = {1, 2, 3}. In this set, 1, 2, and 3 are the elements.
What do the symbols ∈ and ∉ mean?
The symbol ∈ means "belongs to" or "is an element of" (for example, 2 ∈ {1, 2, 3} is true). The symbol ∉ means "does not belong to" or "is not an element of" (for example, 4 ∉ {1, 2, 3} is true).
What is the difference between union (∪) and intersection (∩)?
The union (A ∪ B) combines all elements from both sets into a new set. The intersection (A ∩ B) contains only the elements that are present in both sets at the same time.