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MGF 1106 (4)

Lecture 1

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University of Florida
MGF 1106
Jordan Draper

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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