  ## "Ellipsis" Symbol. . . Shown and Explained Ellipsis Symbol . . .

Background - why symbols are used . . .

Ellipsis Symbols are used as a concise way of giving lengthy

instructions related to numbers and logic.

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 valuable, most frequently used Symbols in
mathematics . . .
:

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

Miscellaneous Symbols - click description Math Symbol for (horizontal) "Ellipsis" - - (Sometimes referred to as dot-dot-dot.)

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  