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2.1:
Basic Set Concepts
Sets:
A set is a collection or group of objects, called elements, that can be clearly defined.
Capital
letters are used to name sets and the elements of the set are enclosed in braces.
Three methods of
representing the elements of a set are [a]
word description
,
where the elements are described in
words (Set N is the set of natural numbers); [b]
roster method,
where each element is listed
separated by commas:
V = {x, y, z}; N = {1, 2, 3, …}; and [c]
setbuilder notation
would describe
the natural numbers as N = {x
x
∈
I, and x > 0}, read N is the set of all x such that x is a natural
number .
The symbol
∈
is used to indicate that an object is a member of a set, and the symbol
∉
indicates that an object is not an element of a set.
Examples:
x
∈
V, m
∉
V.
The empty set or null
set is the set that contains no elements and is represented by {} or
Φ;
it is a subset of every set.
A set
is finite if the number of elements of the set can be counted (0 elements, 5 elements, etc.).
It is
infinite if the number of elements continues to infinity, like the Natural numbers: N = {1, 2, 3, …}.
The three dots indicates that the elements continue in the same pattern.
1.
Use all three types of set notation to show the set of whole numbers, W.
a.
Show whether 5 is a member of W.
b.
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This note was uploaded on 01/04/2012 for the course MGF 1106 taught by Professor Staff during the Fall '08 term at Miami Dade College, Miami.
 Fall '08
 Staff

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