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Definition.
An
object or idea in a set is called an
element (member) of the set.
The symbol
∈
is used to denote that an element is a member of a set and
a slash is put through the symbol
∉
to denote that an object is not a member of a set.
Examples. For the sets A and
B used in the previous example, we have
Definition.
The
null set (empty set) is a set
that has no members. The symbol
Ø
is
used to represent the null set (empty set).
Example.
Ø
=
The collection of people attending MSUM who are 200 years old
Ø =
{ }
Ø
=
{x :
x is a person attending MSUM
who is 200 years old.}
Note
that {Ø
}
does
not symbolize the empty
set; it represents a collection of empty sets.
Definition.
Two sets are equal, if they
have exactly the same elements.
Examples.
Consider the sets A = {a, b, c},
B = {b,
c, a}, C = {a, a, c, b, c}, D = {a,
b,
d}, then
A =
B = C ≠
D.
The sets
A, B, and
C are all equal since they
each have the elements a, b,
and c, and no other elements.
The set D is not equal to the other three sets since
c
∈A
but
c
∉
D.