Symbols are
a concise
way of giving
lengthy
instructions
related to
numbers and
logic.
Symbols are
a communication
tool. Symbols
are used to
eliminate the
need to write
long, plain
language
instructions to
describe
calculations
and other
processes.
For example, a
single symbol
stands for the
entire process
for addition.
The familiar
plus sign
eliminates the
need for a long
written
explanation of
what addition
means and how
to accomplish
it.
The same
symbols are
used worldwide
. . .
The symbols
used in
mathematics are
universal.
The same math
symbols are
used throughout
the civilized
world. In most
cases each
symbol gives
the same clear,
precise meaning
to every
reader,
regardless of
the language
they speak.
The most
valuable,
most
frequently used
Symbols in
mathematics . .
.
The most
important, most
frequently used
Symbols for
Set
Notation
are listed
below.
Symbol
for
"PROPER
(1) Subset
(right) of
Set
(left)"

A
D
means Set
"D"
is a
PROPER
Subset
of Set
"A":
(1)
Every
element
(without
exception)
contained in
Set
"D"
is also present
in Set
"A".
And .
. .
(2)
Set
"D"
CANNOT be
equal to
Set
"A".
(Set
"D"
must have a
smaller number
of elements
than Set
"A")
The math symbol
is
equivalent
to and
is
interchangeable
with
(notice
the equal
sign at
the bottom
edge of
the symbol
is crossed
out,
indicating
the subset
cannot be
equal to
the set).
Both
symbols
mean
exactly
the same
thing: a
"Proper"
Subset.
In contrast,
the subset math
symbol
represents
any
subset,
but not
necessarily
a Proper
Subset.
Item (2),
above,
does not
apply when
the
symbol is
used. If
this
symbol is
used, it
indicates
that the
subset
(labeled
"D"
in the
example
shown
above) and
the set
(labeled
"A"
in the
example
shown
above)
can
be
equal.
Example 1:
, Set
A:
A
=
{
a
,
b,
c
,
d}
Set
D:
D
=
{
a
,
c
}
. . . Both
Set
"D"
and Set
"A"
contain
the
following
elements:
a, c
. . .
All
of the
elements
in Set
"D"
are also
elements
of Set
"A".
. . . Set
"D"
and Set
"A"
are not
equal. Set
"A"
contains
more
elements
than Set
"D".
. . . Set
D
is a
"Proper
Subset"
of Set
A
A
D
Example 2:
, Set
B:
B
=
{1,
3,
9,
11
}
Set
E:
E
=
{
9,
11
}
. . . Both
Set
"E"
and Set
"B"
contain
the
following
elements:
9, 11
. . .
All
of the
elements
in Set
"E"
are also
elements
of Set
"B".
. . . Set
"E"
and Set
"B"
are not
equal. Set
"B"
contains
more
elements
than Set
"E".
. . . Set
E
is a
"Proper
Subset"
of Set
B
B
E
Example 3:
, Set
C:
C
=
{
cat
bird,
dog,
horse,
rabbit
}
Set
F:
F
=
{
rabbit,
cat
}
. . . Both
Set
"F"
and Set
"C"
contain
the
following
elements:
rabbit,
cat
. . .
All
of the
elements
in Set
"F"
are also
elements
of Set
"C".
. . . Set
"F"
and Set
"C"
are not
equal. Set
"C"
contains
more
elements
than Set
"F".
. . . Set
F
is a
"Proper
Subset"
of Set
C
C
F
Note:
the
elements
within
a
SET/SUBSET
can
be
listed
in
any
order.