# Set Theory by ert554898

VIEWS: 1 PAGES: 14

• pg 1
```									 Set Theory

By David Chester
History
• Was created by Georg Cantor, influenced
by Richard Dedekind’s deep logical
thinking.
• Set theory came under fire when it was
first published in an article in August
Crelle’s Journal in 1874.
• Leopold Kronecker was a major opponent
to Crelle’s theories, he didn’t even believe
in pi.
History (continued)
• Set theory gained momentum when
– such as being elements in sets being sets
themselves gave rise to a few paradoxes
– thanks to the excitement of this confusion, set
theory was not abandoned.
• This led to the ZFC set theory which is one
of the foundations of mathematics.
Set?
• A set is a collection of things that can fit in
a category
• Basically everything can be classified into
a set
• I.E. Letters, Numbers, Types of People
• A useful application of sets is seeing
different sizes of infinity
Notation
• Each entry in a set is known as an
element.
• Sets are written using curly brackets ("{"
and "}"), with their elements listed in
between.
    means "element of" ;


   means "not an element of"
Union
• A union set is a combination of two or
more sets
• It contains every element the previous sets
• Union Notation:
• If there is a similar element in each set, it
will only be written once
Union Application
• Set A: {8,7,4,32,23,19,30}
• Set B: {54,87,3,23,44,21}
• Union of Set A and Set B:
–A    B: {3,4,7,8,19,21,23,30,32,44,54,87}
Intersection
• An intersection set is the set of elements
that two or more sets have in common
• It only contains the things that are the
same, nothing else
• Intersection Notation:
•  is called the “empty set.” When two or
more sets have nothing in common.
Intersection Application
• Venn Diagrams are most known type of
sets
• Set A: {65,36,87,45,46,17}
• Set B: {46,36,51,57,28,39}
• Intersection of Set A and Set B:
–A    B: {36,46}
Subsets
• A subset is a set in which every element of
a set, basically the entire set, is part of a
larger set.
• Subset Notation: 
• Not a Subset Notation:  
• Yet if even one element in the smaller set
is not in the bigger set, than the smaller
set is not a subset of the larger set.
Subsets Application
• Set A: {14,11,56}
• Set B: {12,38,14,56,76,11}
• Since B has more elements and every
element in A is in B, A is a subset of B:
A B
Sets of Numbers
• By doing sets of numbers it can be shown that they’re
different sizes of infinity.
• Whole: Positive and Zero, No Fractions
• Integer: Positive, Negative and Zero, No fractions
• Rational: Fractions and Integers
• Irrational: Cannot be expressed as a ratio of two
integers, i.e. pi
• Real numbers: everything above
• Imaginary Numbers: A real number times i
• All of these sets have near infinite numbers in them yet
most of them are subsets meaning there is at least one
set of infinity that is greater than another set, i.e.
Rational larger than whole.
Sets of Numbers Application

(Selditch,4)
Bibliography
• http://en.wikipedia.org/wiki/Set_theory
• http://www.math.niu.edu/~rusin/known-
math/index/03EXX.html
• http://www.geocities.com/basicmathsets/
• http://www-history.mcs.st-
and.ac.uk/history/HistTopics/Beginnings_o
f_set_theory.html

```
To top