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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