🔗
Sets
★☆☆☆☆Elementary
📖Definition
A set is a collection of distinct, well-defined objects. It's one of the most fundamental concepts in mathematics.
📐Formulas
A ∪ B = x : x ∈ A or x ∈ B
Union
A ∩ B = x : x ∈ A and x ∈ B
Intersection
A - B = x : x ∈ A and x ∉ B
Difference
|A ∪ B| = |A| + |B| - |A ∩ B|
Inclusion-exclusion principle
✏️Examples
예제 1
If A = {1, 2, 3} and B = {2, 3, 4}, find A ∪ B and A ∩ B.
📜History
Discovered by: Georg Cantor (1874)
Cantor founded set theory while studying how to compare sizes of infinite sets.
⚡Applications
Databases
SQL UNION, INTERSECT operations
Programming
Set data structure
Logic
Truth sets of propositions
#집합#이산수학#set#discrete math