Ellipsis
Symbols are used as
a
concise
way of giving
lengthy

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.

The
most important, most
frequently used
*Miscellaneous*
symbols are listed
below.

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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