Introduction to Sets
A set is simply a collection of distinct objects with no repetition. For example, {1, 2, 3, 4} is a valid set, but {1, 1, 2, 3, 4} isn't because 1 appears twice. The different objects in a set are called elements.
Sets are typically written using roster notation - listing elements inside curly braces like {1, 2, 3, 4}. The order doesn't matter, so {3, 1, 2} equals {1, 2, 3}. When an element belongs to a set, we use the symbol ∈ (epsilon) to show membership. For instance, if A = {1, 2, 3}, then 2 ∈ A means "2 belongs to A."
The cardinality of a set is the number of elements it contains, written as n(S). Sets can be finite (limited number of elements) or infinite (unlimited). A set can be a subset of another set if all its elements are contained in the larger set. Remember, every set has the empty set {∅} as a subset, and every set is a subset of itself.
Quick Tip: When thinking about sets, picture organizing your favorite items. Just as you wouldn't count the same item twice in your collection, sets don't repeat elements!
