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MGF 1106
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Jordan Draper
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Lecture

# Lecture 1

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University of Florida

Mathematics

MGF 1106

Jordan Draper

Summer

Description

Sets
Set = container/box
Elements- what are in the set
o ex. Monday, Tuesday, Wednesday, Thursday, Friday } set of the days of the week
Roster form- delineates a set
o use { }
o not a set ( )
o not a set [ ]
Natural numbers- counting numbers
o N = {1,2,3,4,…}
Set builder notation
o ex. A = {x | x ≥ 0}
reads as “A equals the set of x such that x is greater than or equal to 0”
o ex. A = {x | x ≥ 0, x ∈N}
reads as “A equals the set of x such that x is greater than or equal to 0 and
x is an element of the natural numbers”
V= {a,e,i,o,u} C= {{a},{e,i,o,},{u}}
o Is a∈V? yes
o Is {a}∈C? yes
o Is {a}∈V? no
o Is i∈C? no
Finite set- can count all items in the set
o ex. {1,2,3,4}
Infinite set- doesn’t end
o ex. the natural numbers
Inclusive- contains 2 endpoints
o ex. between 4 and 6 inclusive- answer could be 4,5, or 6
A=B iff (if and only if) everything in A is in B and everything in B is in A
o ex. A= {t,r,a,c} B= {c,a,t,r}
Is A=B? yes
o ex. A= {{t},r,a,c} B= {c,a,t,r}
Is A=B? no
Cardinal number- size of set

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