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A
set
is
a collection of objects from a universe.
The objects are called
members
or
elements
.
They are not in any order, despite how they
may be written, nor may sets contain
duplicate members.
Sets may be denoted in several ways:
(1). By enumeration, if finite. E.g. {1,2,3}
(Same as {2,1,3} — same as {1,1,2,3})
(2). By enumeration with dots of ellipses,
where obvious. {2,4,6 . .}
(3). By use of a propositional function:
{x  x>3} (Need to know universe!)
Or in
general,
{x  P(x)} or “the set of all elements that make
P true.”
E.g. {xx>3} = {4, 5, . .} in domain of integers
1
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View Full DocumentDefine: x
∈
S
to mean “x is an element of S.”
Note that x
∈
S is a proposition. We also define
x
∉
S to mean –(x
∈
S) or “x is not an element
of S.”
Define S as “cardinality of S” or the number
of elements in S.
Define: S
⊆
T as “S is a subset of T”
S
⊆
T iff
2200
x(x
∈
S > x
∈
T)
Define: S=T
iff S and T contain the same
elements, or iff
2200
x(x
∈
S <>x
∈
T)
2
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 Spring '08
 WATKINS

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