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continuation symbol

The continuation symbol is used to indicate extension of a sequence or set , or to imply the existence of intermediate elements in a sequence or set. The symbol consists of three periods placed one after another (...).

When the continuation symbol is used in a sequence or set, a sufficient number of elements in that sequence or set should be listed so as to make it obvious what the continuation symbol represents. The following are examples of proper use of the continuation symbol:

S = 1, 2, 3, ...
X = {..., -3, -2, -1}
Y = {-999, -998, -997, ..., 997, 998, 999}
W = 1, 1/2, 1/3, 1/4, 1/5, ...

In these examples, the first and last items are sequences of numbers, and the middle two items are sets of numbers. The sequences and sets consist of discrete elements, so the continuation symbol serves as a fill-in for a list, such as the set of all integer s between and including -999 and 999. The continuation symbol is sometimes used for sequences or sets of variables, as long as it is clear what the variables beyond the last listed variable represent.

The continuation symbol is occasionally used to indicate that a sequence of numbers continues forever, even if the numbers are not explicitly defined. For example, a nonterminating, nonrepeating decimal such as the square root of 2 (or 2 1/2 ) can be represented in this fashion:

2 1/2 = 1.414213562373 ...

The continuation symbol is not used as a filler-in for continuous sets, such as the set of all real numbers between and including -999 and 999.

Also see Mathematical Symbols .

This was last updated in September 2005
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