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In mathematics, summation is the addition of a sequence of numbers, called addends or summands; the result is their sum or total.Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials and, in general, elements of any type of mathematical objects on which an operation denoted "+" is defined.
If a single term x appears in a sum n times, then the sum is the product of n and x. If n is not a natural number , the product may still make sense; for example, multiplication by −1 yields the additive inverse of a number.
A zero-sum game is also called a strictly competitive game, while non-zero-sum games can be either competitive or non-competitive. Zero-sum games are most often solved with the minimax theorem which is closely related to linear programming duality, [5] or with Nash equilibrium. Prisoner's Dilemma is a classic non-zero-sum game. [6]
The concept of a decimal digit sum is closely related to, but not the same as, the digital root, which is the result of repeatedly applying the digit sum operation until the remaining value is only a single digit. The decimal digital root of any non-zero integer will be a number in the range 1 to 9, whereas the digit sum can take any value.
This article relies largely or entirely on a single source. ... In mathematics, an empty sum, or nullary sum, [1] is a summation where the number of terms is zero.
For example, the Ky Fan-k-norm is the sum of first k singular values, the trace norm is the sum of all singular values, and the Schatten norm is the pth root of the sum of the pth powers of the singular values. Note that each norm is defined only on a special class of operators, hence singular values can be useful in classifying different ...
The identity permutation is defined by () = for all elements , and can be denoted by the number , [a] by =, or by a single 1-cycle (x). [ 15 ] [ 16 ] The set of all permutations of a set with n elements forms the symmetric group S n {\displaystyle S_{n}} , where the group operation is composition of functions .
The subset sum problem (SSP) is a decision problem in computer science. In its most general formulation, there is a multiset of integers and a target-sum , and the question is to decide whether any subset of the integers sum to precisely . [1] The problem is known to be NP-complete.