Functions Flashcards

Covers total vs partial functions, injection, bijection and surjection

1
Q

partial function

A

a function that is defined on a subset of a set, rather than the entire set

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

total function

A

a function defined for every element of the domain

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

surjective functions are also known as

A

onto functions

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

surjective functions have a range equal to…

A

their codomain

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

example of a violation of a property of surjective functions

A

there is some element of the codomain of set A, which does not map onto an input value.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

example of a violation of a property of total functions

A

there is some value in the set that has an undefined output

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

total functions refer to the completeness of the _______ while partial functions refer to the completeness of the ________

A

domain, codomain

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

how to prove injectivity

A

confirm it is a total function and show that the function and its inverse are mutually inverse

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

how to prove bijectivity

A

confirm it is total, then confirm it is has an inverse which is also total

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

a bijection is injective in

A

both directions

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

in the function definition f: A -> B, what are the purposes of A and B?

A

domain is the set A and the codomain is the set B

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

f : a ⊢> b is equivalent to ____ which is also called ?

A

(a, b) , maplets

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

if f(a) = b, a is the _________ of the function

A

argument

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

if f(a) = b, b is the _____ of the function

A

value

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

what is arity

A

the number of arguments a function takes

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

common binary functions are often written as

17
Q

the image is always a subset of…

A

the codomain

18
Q

give that f(x) = x^2, what is the preimage of {1}?

19
Q

express the set of students who have achieved more than 70 as a preimage of the set ‘score’

A

score-1({n ∈ ℕ : n > 70})