Functions Flashcards
Covers total vs partial functions, injection, bijection and surjection
partial function
a function that is defined on a subset of a set, rather than the entire set
total function
a function defined for every element of the domain
surjective functions are also known as
onto functions
surjective functions have a range equal to…
their codomain
example of a violation of a property of surjective functions
there is some element of the codomain of set A, which does not map onto an input value.
example of a violation of a property of total functions
there is some value in the set that has an undefined output
total functions refer to the completeness of the _______ while partial functions refer to the completeness of the ________
domain, codomain
how to prove injectivity
confirm it is a total function and show that the function and its inverse are mutually inverse
how to prove bijectivity
confirm it is total, then confirm it is has an inverse which is also total
a bijection is injective in
both directions
in the function definition f: A -> B, what are the purposes of A and B?
domain is the set A and the codomain is the set B
f : a ⊢> b is equivalent to ____ which is also called ?
(a, b) , maplets
if f(a) = b, a is the _________ of the function
argument
if f(a) = b, b is the _____ of the function
value
what is arity
the number of arguments a function takes
common binary functions are often written as
infix
the image is always a subset of…
the codomain
give that f(x) = x^2, what is the preimage of {1}?
{1,-1}
express the set of students who have achieved more than 70 as a preimage of the set ‘score’
score-1({n ∈ ℕ : n > 70})
