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"Ellipsis"

- Symbol Shown and Explained -

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Background - why Ellipsis Symbols are used. . .

Symbols are a concise way of giving lengthy instructions related to numbers and logic.

Math Symbols are an invention, not a discovery. They are a communication tool. Symbols are 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.
Math - Ellipsis Math Symbol for (horizontal) "Ellipsis" - (Sometimes referred to as dot-dot-dot.)
In mathematics, inserting an ". . ." 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: Math - Ellipsis (horizontal) (2) Vertical: Math - Ellipsis (vertical) (3) Diagonal: Math - Ellipsis (diagonal)
Example 1: Math - Ellipsis (horizontal) , 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: Math - Pi Symbol = 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: Math - Ellipsis (vertical) , Vertical Use the vertical ellipsis math symbol with a table or matrix Math - Ellipsis (vertical) - example
Example 3: Math - Ellipsis (diagonal) , Diagonal Use the diagonal ellipsis math symbol with a table or matrix Math - Ellipsis (diagonal) - example




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