CS2130:Section 5.1

What is a function?

Unlike previous math classes, the Vertical Line Test is not used in this course

Terms

• Domain - Inputs of a function
• Range - Outputs of a function

Types of functions

Todo: add graphics to go along with these functions

Into

A visual representation of the Into function

Everything in A is used, and goes to only one element in B

Onto

A visual representation of the Onto function

Everything in B is used

1-to-1

A visual representation to the 1-to-1 function

Any element in B can go to at most one element in A

Invertible

Also known as a bijection

A visual representation of the Invertible/Bijection function

Both 1-to-1 & onto

Symbols

Negation

${\overline {A}}$ = $U-A$

Unsure if this is the correct name

Everything in the Universe except what is inside A

Count Of

$|A|$

Count of elements inside A

Union

$A\bigcup B$

A combination of both sets

Intersection

$A\bigcap B$

A set containing what is in both sets

Element

$1\in B$

$1$ is an element of $B$

Subset

$\{1\}\subseteq B$

1 is a subset of $B$

Notes

1. The total number of subsets a set can have is equivalent to $2^{|A|}$

Symmetric Difference

$A\oplus B$

Everything in $A$ but not in $B$

Effectively a unique filter

Example

$A\oplus B=(A\bigcup B)-(A\bigcap B)$

Empty Set

$\varnothing$

An empty set

Notes

1. An Empty Set is a Subset of any set, but not an element of every set
2. An Empty Set is only an element of a set if explicitly a part of the set (you won't see this)