Lecture 3 - Functions, Sequences and Relations Flashcards
1
Q
Of what is a function f : X -> Y a subset?
A
X x Y
2
Q
In what cases would a statement not be considered a function?
A
- If an element in X did not map to any value in Y (domain -> codomain)
- If one element in X mapped to multiple elements in Y
3
Q
How do we test to see if a statement is a function?
A
The Vertical Line Test
4
Q
How do we test to see if a function is one to one?
A
The Horizontal Line Test
5
Q
What does it mean for a function f from X->Y to be onto?
A
That all elements in the codomain map to an element in the domain.
6
Q
What is a function that is both one-to-one and onto?
A
A bijection
7
Q
What does a binary operator on a set X do?
A
It associates with each ordered pair of elements in X one element in X
8
Q
What does a unary operator on a set X do?
A
It associates with each single element of X one element in X
9
Q
What type of diagram shows if a statement is one-to-one, onto, or a function?
A
Arrow diagram
