N := Natural Number
Z := Integer
Q := Rational Number
R := Real Number
C := Complex Number
When two sets have no elements in common, they are said to be disjoint
Subsets of are called relations
A relation is well-defined if each element in the domain is assigned to a unique element in the range.
Surjective or onto
each element in B has an A
Injective or One-to-one
- Countable: can be put in 1-1 correspondence with positive integers
- Rational Numbers
- Read line, plane
A map that is both one-to-one and onto is called bijective.
If S is any set, we will use ids or id to denote the identity mapping from S to itself.
Define this map by id(s)= s for all s S.
A mapping is invertible if and only if it is both one-to-one and onto.
- AND: Set Intersection
- OR: Set Union
- XOR: Symmetric Difference