In mathematics, the empty sum, or nullary sum, is the result of adding no numbers. Its numerical value is zero.
This fact is especially useful and helpful in discrete mathematics and algebra. A simple, well known case is that 0a = 0 -- multiplication of any number a by zero always results in zero, because you have added zero copies of a, which is no numbers at all. Many people find the empty sum easier to grasp than the empty product -- the product of no numbers -- whose value is not zero, but one.
In mathematics, the emptysum, or nullary sum, is the result of adding no numbers.
A simple, well known case is that 0a = 0 -- multiplication of any number a by zero always results in zero, because you have added zero copies of a, which is no numbers at all.
Many people find the emptysum easier to grasp than the empty product -- the product of no numbers -- whose value is not zero, but one.
The value of the emptysum of numbers is equal to the additive identity number, 0.
Nevertheless, it is sometimes natural to define that the Cartesian product of an empty collection of sets equals to a set with one element; so it may mean that e.g.
This is version 8 of empty product, born on 2004-11-08, modified 2005-03-27.
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