Grant: add images

2024-01-24T01:16:27Z

add images

← Older revision		Revision as of 01:16, 24 January 2024
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	==== Into ====		==== Into ====
			[[File:Into-set.svg\|thumb\|150x150px\|A visual representation of the Into function]]
	Everything in A is used, and goes to only one element in B		Everything in A is used, and goes to only one element in B
			{{Clear}}

	==== Onto ====		==== Onto ====
			[[File:Onto-set.svg\|thumb\|150x150px\|A visual representation of the Onto function]]
	Everything in B is used		Everything in B is used
			{{Clear}}

	==== 1-to-1 ====		==== 1-to-1 ====
			[[File:1-to-1-set.svg\|thumb\|150x150px\|A visual representation to the 1-to-1 function]]
	Any element in B can go to <u>at most</u> one element in A		Any element in B can go to <u>at most</u> one element in A
			{{Clear}}

	==== Invertible ====		==== Invertible ====
	''Also known as a bijection''		''Also known as a bijection''
			[[File:Bijection-set.svg\|thumb\|150x150px\|A visual representation of the Invertible/Bijection function]]
	Both 1-to-1 & onto		Both 1-to-1 & onto
			{{Clear}}

	== Symbols ==		== Symbols ==

Grant: Create section 5.1

2024-01-23T03:03:17Z

Create section 5.1

New page

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

==== Onto ====
Everything in B is used

==== 1-to-1 ====
Any element in B can go to <u>at most</u> one element in A

==== Invertible ====
''Also known as a bijection''

Both 1-to-1 & onto

== Symbols ==

=== Negation ===
<math>\overline{A}</math> = <math>U - A</math>

''Unsure if this is the correct name''

Everything in the Universe except what is inside A

=== Count Of ===
<math>|A|</math>

Count of elements inside A

=== Union ===
<math>A \bigcup B</math>

A combination of both sets

=== Intersection ===
<math>A \bigcap B</math>

A set containing what is in both sets

=== Element ===
<math>1 \in B</math>

<math>1</math> is an element of <math>B</math>

=== Subset ===
<math>\{1\} \subseteq B</math>

1 is a subset of <math>B</math>

==== Notes ====

# The total number of subsets a set can have is equivalent to <math>2^{|A|}</math>

=== Symmetric Difference ===
<math>A \oplus B</math>

Everything in <math>A</math> but not in <math>B</math>

Effectively a unique filter

===== Example =====
<math>A \oplus B = (A \bigcup B) - (A \bigcap B) </math>

=== Empty Set ===
<math>\varnothing</math>

An empty set

===== Notes =====

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

CS2130:Section 5.1 - Revision history

Grant: add images

Grant: Create section 5.1