Functions Flashcards
What is a function?
A function is something that takes in an input and returns an output.
What is another name for an input?
Domain
What is another name for an output?
Co-domain
What is a pair?
A pair is the domain and co-domain given a function. Denoted (a,b)
What is a total function?
An assignment of exactly one element of set A to set B given a function
What is a partial function?
An assignment of at most one element of set A to set B given a function
What is the co-domain compared to the range?
The co-domain is the set of all possible values which can come out as a result but the range is the set of values that actually come out.
What is the image?
The image of a function is the set of values produced from the subset of a domain.
What is the pre-image?
The pre-image of a function is the set of arguments that produce a given subset.
What is true for the inverse of a total function?
f-1(B) = A, this does not hold for a partial function.
What does arity mean?
The number of arguments taken by a function
What is an injection function?
An injection function produces different outputs when given different inputs and produce the same output providing you use the same input.
What is a surjective function?
A function is surjective if all of the elements of the co-domain can be produced. Therefore the co-domain and range are equal.
What is a bijective function?
A function is bijective if it is both an injection and a surjection.
If f: A -> B and g: B -> C what does g . f give?
g . f: A -> C
