Definitions for empty sum
emp·ty sum

WiktionaryRate this definition:0.0 / 0 votes

1. empty sumnoun

   The result of adding no numbers (defined in order to be able to extend certain mathematical concepts, such as the sum of numbers, to the case where = 0).

WikipediaRate this definition:0.0 / 0 votes

1. Empty sum

   In mathematics, an empty sum, or nullary sum, is a summation where the number of terms is zero. The natural way to extend non-empty sums is to let the empty sum be the additive identity. Let a 1 {\displaystyle a_{1}} , a 2 {\displaystyle a_{2}} , a 3 {\displaystyle a_{3}} , ... be a sequence of numbers, and let s m = ∑ i = 1 m a i = a 1 + ⋯ + a m {\displaystyle s_{m}=\sum _{i=1}^{m}a_{i}=a_{1}+\cdots +a_{m}} be the sum of the first m terms of the sequence. This satisfies the recurrence s m = s m − 1 + a m {\displaystyle s_{m}=s_{m-1}+a_{m}} provided that we use the following natural convention: s 0 = 0 {\displaystyle s_{0}=0} . In other words, a "sum" s 1 {\displaystyle s_{1}} with only one term evaluates to that one term, while a "sum" s 0 {\displaystyle s_{0}} with no terms evaluates to 0. Allowing a "sum" with only 1 or 0 terms reduces the number of cases to be considered in many mathematical formulas. Such "sums" are natural starting points in induction proofs, as well as in algorithms. For these reasons, the "empty sum is zero" extension is standard practice in mathematics and computer programming (assuming the domain has a zero element). For the same reason, the empty product is taken to be the multiplicative identity. For sums of other objects (such as vectors, matrices, polynomials), the value of an empty summation is taken to be its additive identity.

WikidataRate this definition:0.0 / 0 votes

1. Empty sum

   In mathematics, an empty sum, or nullary sum, is a summation involving no terms at all. The value of any empty sum of numbers is conventionally taken to be zero. For summations defined in terms of addition of other values than numbers, in general of values in some given Abelian group, the value of an empty summation is taken to be the zero element of that group. An empty sum can arise in particular for expressions of the form when ; in such case the summation has value 0. A situation similar to an empty summation can arise for other operations than addition; notably, its counterpart for multiplication is an empty product, a product of no factors at all. In such cases the convention of a zero result does not apply; indeed the value of an empty product of numbers is taken to be one, the neutral element for multiplication.

How to pronounce empty sum?

1. Alex

   US English

   David

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   Mark

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   Daniel

   British

   Libby

   British

   Mia

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   Karen

   Australian

   Hayley

   Australian

   Natasha

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   Indian

   Priya

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   Neerja

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   Zira

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   Oliver

   British

   Wendy

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   Fred

   US English

   Tessa

   South African

How to say empty sum in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of empty sum in Chaldean Numerology is: 8

2. Pythagorean Numerology

   The numerical value of empty sum in Pythagorean Numerology is: 6

References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Empty_Sum
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Empty_Sum
3. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=empty sum