4.1 Definition of functions
- A function f that maps elements of a set X to elements of a set Y, is a subset of X x Y such that
for every e ∈ X, there is exactly one y ∈ Y for which (x, y) ∈ f
- F: X → Y is the notation that f is a function from X to Y
- Set X is called domain of f, and the set Y is the target of f (aka co-domain)
- F maps x to y (or (x, y) ∈ f) also denoted as f(x) = y
- If f maps an element of the domain to zero elements or more than one element of the target, then f
is not well defined
- An element y is in the range of f if and only if there is an x ∈ X such that (x, y) ∈ f
- Finite domain, in an arrow diagram, there is exactly one arrow point out of every element of the
domain
- Two functions, f and g, are equal if f and g have the same domain and target, and f(x) = g(x) for
every element x in the domain
- A function f that maps elements of a set X to elements of a set Y, is a subset of X x Y such that
for every e ∈ X, there is exactly one y ∈ Y for which (x, y) ∈ f
- F: X → Y is the notation that f is a function from X to Y
- Set X is called domain of f, and the set Y is the target of f (aka co-domain)
- F maps x to y (or (x, y) ∈ f) also denoted as f(x) = y
- If f maps an element of the domain to zero elements or more than one element of the target, then f
is not well defined
- An element y is in the range of f if and only if there is an x ∈ X such that (x, y) ∈ f
- Finite domain, in an arrow diagram, there is exactly one arrow point out of every element of the
domain
- Two functions, f and g, are equal if f and g have the same domain and target, and f(x) = g(x) for
every element x in the domain
