SET003 · Sets, relations & logic · Classes 9–11
Empty set
The empty set ∅ (or { }) has no elements. Its cardinal number is 0. There is only one empty set.
∅Empty set
📐 Formula
∅ = { }, n(∅) = 0
✏️ Worked example
{x ∈ ℕ : x < 1} = ∅, because no natural number is less than 1. Raise k and the set fills up.
🌍 Where it is used
Saying 'no solutions' precisely, e.g. {x : x² = −1, x real} = ∅.
❓ Quick check
Which set is empty?
🏋️ Practice
EasyIs {0} the empty set?
Answer: No: it has one element, 0
Mediumn(∅) = ?
Answer: 0
ChallengeGive an empty set from real life.
Answer: e.g. months with 32 days