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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 0''a'' = 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.

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References

References

★ A.E. Ingham, contributor R C Vaughan, ''The Distribution of Prime Numbers'', Cambridge University Press, 1990, ISBN 0-521-39789-8