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- Empty_sum abstract "In mathematics, an empty sum, or nullary sum, is a summation where the number of terms is zero. By convention, the value of any empty sum of numbers is zero. Let a1, a2, a3,... be a sequence of numbers, and letbe the sum of the first m terms of the sequence. Thenfor all m = 1,2,... provided that we use the following conventions: and . In other words, a "sum" with only one term evaluates to that one term, while a "sum" 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 convention" is standard practice in mathematics and computer programming. For the same reason, the empty product is taken to be one, the neutral element for multiplication.For summations defined in terms of addition of other values than numbers (such as vectors, matrices, polynomials), 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.".
- Empty_sum wikiPageID "209748".
- Empty_sum wikiPageRevisionID "601579582".
- Empty_sum hasPhotoCollection Empty_sum.
- Empty_sum subject Category:Arithmetic.
- Empty_sum subject Category:Zero.
- Empty_sum comment "In mathematics, an empty sum, or nullary sum, is a summation where the number of terms is zero. By convention, the value of any empty sum of numbers is zero. Let a1, a2, a3,... be a sequence of numbers, and letbe the sum of the first m terms of the sequence. Thenfor all m = 1,2,... provided that we use the following conventions: and . In other words, a "sum" with only one term evaluates to that one term, while a "sum" with no terms evaluates to 0.".
- Empty_sum label "Empty sum".
- Empty_sum label "Leere Summe".
- Empty_sum label "Soma vazia".
- Empty_sum label "Somma vuota".
- Empty_sum label "Somme vide".
- Empty_sum label "Suma vacía".
- Empty_sum sameAs Leere_Summe.
- Empty_sum sameAs Suma_vacía.
- Empty_sum sameAs Somme_vide.
- Empty_sum sameAs Somma_vuota.
- Empty_sum sameAs Soma_vazia.
- Empty_sum sameAs m.01dslw.
- Empty_sum sameAs Q1812158.
- Empty_sum sameAs Q1812158.
- Empty_sum wasDerivedFrom Empty_sum?oldid=601579582.
- Empty_sum isPrimaryTopicOf Empty_sum.