8/22/2007
1
LING 178
Introduction
Set theory is fundamental to
mathematics and has a number of direct
applications in linguistics.
We start by characterizing briefly the
most important concepts in the field of
set theory.
Set (definition)
A
set
is a group of objects represented
as a unit.
A set may contain any type of object,
numbers, words, drawings, etc. they are
called the
members
(or
elements
) of
the set
.
Sets are referred to with CAPITAL letters
(the set A).
Members of a set in lowercase (a is a
member of A).
Examples of sets …
34
12
119
98
65
1
Set A
Set B
Set C
terrible
tortoise
tundra
tiddlywink
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Beware!
There is a difference between x and {x}.
What is it?
The first, x, is an
element
.
The second, {x}, is a
set
containing one
element.
For mathematical and other purposes,
these two cases are distinct.
Enumeration
A set can be described as a
list
of the
objects it contains (a list of its members).
This is called
enumeration
.
A list is put between braces:
{ }
.
A = {1, 12, 34, 65, 98, 119}
C = {terrible, tortoise, tundra, tiddlywink}
The order of objects in a list does not
matter.
Description
We may use a
description
of the
members of a set rather than an
enumeration.
T = {x  x is an English word starting with „t‟}
“T is the set of all English words starting
with the letter „t‟”.
Elements
The objects in a set are called
elements
or
members
.
∈
means ‘is an element of’
∉
means ‘is not an element of’
A = {1, 12, 34, 65, 98, 119}
34
∈ A
35
∉ A
Questions…
Q:
Can a set have any number of
elements?
A:
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 Spring '08
 DeHaan
 Set Theory, Empty set

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