Cardinal of an empty set.

  • The number zero is a natural number.
  • The number zero is associated with a point on a number line that is the border between positive and negative numbers.
  • The number zero is an even number.
  • When zero is the exponent of a number, it transforms this number into a one: \(n^{0}\) = 1.
  • The number zero is the identity element of addition: n + 0 = 0 + n = n.
  • The number zero is the absorbing element of multiplication: n × 0 = 0 × n = 0.

Historical Note

The digit zero was the last one to be added to our numeral system. In fact, before learning Arabic numerals (borrowed from the Hindus), Europeans used Roman numerals, which have no symbol to represent “nothing”. First represented by a dot, the symbol in the shape of an O appeared in a document printed in 1491, in a book by Philippi Calandri called De Arithmetica Opusculum.

The word zero itself comes from the Arabic word Sifr (pronounced chifr) which means both nothing or numeral sign.

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