Math 100
Talking about sets
Martin H. Weissman
1.
Examples of sentences about sets
Let
S
=
{
2
,
5
,
{
2
}
,
{
3
,
4
}}
.
The following are true sentences about
S
, involving the phrase “is an element of”:
(1) 2 is an element of
S
. Symbolically, 2
∈
S
.
(2) 5 is an element of
S
. Symbolically, 5
∈
S
.
(3)
{
2
}
is an element of
S
. Symbolically,
{
2
} ∈
S
.
(4)
{
3
,
4
}
is an element of
S
. Symbolically,
{
3
,
4
} ∈
S
.
(5) 3 is
not
an element of
S
. Symbolically, 3
6∈
S
.
(6)
{
2
,
5
}
is
not
an element of
S
. Symbolically,
{
2
,
5
} 6∈
S
.
The following are true sentences, involving counting elements of
S
.
(1) There are four elements of
S
. Symbolically, #
S
= 4.
(2) There are two elements of
S
, which are numbers. There is not a nice way of saying this symbolically.
(3) There is one element of
S
, which is an even number. There is not a nice way of saying this symboli
cally.
The following are true sentences, involving the phrase “is a subset of”:
(1) The empty set is a subset of
S
. Symbolically,
∅ ⊂
S
.
(2)
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 Fall '08
 Weissman
 Set Theory, Sets, Basic concepts in set theory

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