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The definition of number in Mathematics has developed throughout the ages.

When What Where
Circa 20000 B.C. Whole numbers Africa - How old is Mathematics?
Circa 2800 B.C. Rational numbers India
800 - 500 B.C. Irrational numbers India
5th Century B.C. zero India
100 B.C. Negative numbers China
16th Century Complex numbers Italy - Niccolo Fontana Tartaglia, Gerolamo Cardano
1761 Transcendental numbers Switzerland - Johann Heinrich Lambert
1843 Quaternions Ireland - Sir William Rowan Hamilton
1895 Transfinite numbers Germany - Georg Cantor
1966 Hyperreal numbers U.S.A. - Abraham Robinson

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