Math Symbols are
a communication
tool. Symbols are an
invention which is
used to eliminate
the need to write
long, plain language
instructions to
describe
calculations and
other processes.

In mathematics,
inserting
". .
."
generally means
two things:

(1)
Information
has been
omitted
intentionally
to save
space.

(2) To show
that an
established
pattern
continues
.

Three types of
ellipsis are
commonly
used:

(1)
Horizontal
:

(2)
Vertical
:

(3)
Diagonal
:

Example
1:
,
Horizontal

*Set A:*
A
=
{a, b,
c,
. .
.
, x, y,
z}

Set
"A"
contains all
the letters of
the alphabet,
in alphabetical
order.

The
"..."
is used to:

1)
show the
letters
"d"
through
"w"
belong to the
set, even
though they are
not listed
individually;
and
2) show
that the
unlisted
letters are
arranged
alphabetically
(the pattern
already
established by
the a, b, c
order).

*Set B:*
B
=
{2, 4,
6,
. .
.
, 22, 24,
26}

Set
"B"
contains all
the even
numbers from 2
through 26,
listed from
lowest to
highest.

The
"..."
is used to:

1)
show the even
numbers
"8"
through
"20"
belong to the
set, even
though they are
not listed
individually;
and
2) show
that the
unlisted
numbers are
arranged lowest
to highest (the
pattern already
established by
the 2, 4, 6
arrangement).

*Calculation:*
X
=
5+6+7+
^{. .
.}
+11+12+13

"X"
equals the sum
of all the
numbers between
5 and 13.

The
"^{...}"
is used to:

1)
show the
numbers
"8"
through
"10"
must be
included, even
though they are
not listed
individually;
and
2) show
that the
unlisted
numbers are
added to the
listed numbers
(the pattern
already
established by
1+2+3+ ).

*Note:*
Because
a calculation
is involved,
the
"^{...}"
is raised to
the level of
the +
sign.

*Repeating
Decimal:*
Y =
7.
121212
. .
.

(rational
number)

The
decimal portion
of the number
is a
non-terminating
sequence which
repeats the
numbers
"12"
over and over,
forever.

The
"^{...}"
is used to:

1)
show the
decimal portion
of the number
contains more
numbers than
those listed;
and
2) show
the numbers
"12"
are repeated
over and over
in that order,
endlessly.

Non
*-Repeating
Decimal:*
=
3.
14159
. .
.

(irrational
number)

The
decimal portion
of an
irrational
number such as
Pi is a
non-terminating
sequence. It
has no pattern
which can be
repeated.

The
"^{...}"
is used to:

1)
show the
decimal portion
of the number
contains more
numbers than
those
listed.

*Note:*
This is
an exception.
Irrational
numbers such as
Pi have
non-terminating
decimals.
However, there
is no repeating
pattern. The
"..."
is used
anyway.

Example
2:
,
Vertical

Use the
vertical
ellipsis math
symbol with a
table or
matrix

Example
3:
,
Diagonal

Use the
diagonal
ellipsis math
symbol with a
table or
matrix

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