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  2. Empty sum - Wikipedia

    en.wikipedia.org/wiki/Empty_sum

    In mathematics, an empty sum, or nullary sum, [1] is a summation where the number of terms is zero. The natural way to extend non-empty sums [ 2 ] 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

  3. Subset sum problem - Wikipedia

    en.wikipedia.org/wiki/Subset_sum_problem

    Let A be the sum of the negative values and B the sum of the positive values; the number of different possible sums is at most B-A, so the total runtime is in (()). For example, if all input values are positive and bounded by some constant C , then B is at most N C , so the time required is O ( N 2 C ) {\displaystyle O(N^{2}C)} .

  4. Empty product - Wikipedia

    en.wikipedia.org/wiki/Empty_product

    In mathematics, an empty product, or nullary product or vacuous product, is the result of multiplying no factors.It is by convention equal to the multiplicative identity (assuming there is an identity for the multiplication operation in question), just as the empty sum—the result of adding no numbers—is by convention zero, or the additive identity.

  5. Direct sum of groups - Wikipedia

    en.wikipedia.org/wiki/Direct_sum_of_groups

    The group operation in the external direct sum is pointwise multiplication, as in the usual direct product. This subset does indeed form a group, and for a finite set of groups {H i} the external direct sum is equal to the direct product. If G = ΣH i, then G is isomorphic to Σ E {H i}. Thus, in a sense, the direct sum is an "internal ...

  6. Aggregate function - Wikipedia

    en.wikipedia.org/wiki/Aggregate_function

    Sum; Others include: Nanmean (mean ignoring NaN values, also known as "nil" or "null") Stddev; Formally, an aggregate function takes as input a set, a multiset (bag), or a list from some input domain I and outputs an element of an output domain O. [1] The input and output domains may be the same, such as for SUM, or may be different, such as ...

  7. Damian Lillard reportedly signs lifetime contract extension ...

    www.aol.com/damian-lillard-reportedly-signs...

    Fresh off winning the NBA Cup, Damian Lillard is joining an exclusive club. The Milwaukee Bucks point guard has agreed to a lifetime contract extension with Adidas, per ESPN's Shams Charania ...

  8. Illinois quick hits: Crimo video confession admissible; pay ...

    www.aol.com/news/illinois-quick-hits-crimo-video...

    Crimo video confession admissible A judge has ruled that a video confession given by the man accused of shooting and killing seven people at an Independence Day parade in Highland Park two years ...

  9. Integer partition - Wikipedia

    en.wikipedia.org/wiki/Integer_partition

    The only partition of zero is the empty sum, having no parts. The order-dependent composition 1 + 3 is the same partition as 3 + 1, and the two distinct compositions 1 + 2 + 1 and 1 + 1 + 2 represent the same partition as 2 + 1 + 1. An individual summand in a partition is called a part. The number of partitions of n is given by the partition ...