Principle of Inclusion-Exclusion in Mathematics

The name comes from the idea that the principle is based on over-generous inclusion, followed by compensating exclusion. This concept is attributed to Abraham de Moivre (1718); but it first appears in a paper of Daniel da Silva (1854), and later in a paper by J. J. Sylvester (1883). Sometimes the principle is referred to as the formula of Da Silva, or Sylvester due to these publications. The principle is an example of the sieve method extensively used in number theory and is sometimes referred to as the sieve formula, though Legendre already used a similar device in a sieve context in 1808.