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* ''hyperbolic complex numbers'', J.C. Vignaux (1935)
* ''bireal numbers'', U. Bencivenga (1946)
* ''real hyperbolic numbers'', N. Smith (1949)<ref>{{cite thesis |last=Smith |first=Norman E. |title=Introduction to Hyperbolic Number Theory |type=MA |publisher=McGill University |year=1949 |url=https://escholarship.mcgill.ca/concern/theses/1544bs68g }}</ref>
* ''approximate numbers'', Warmus (1956), for use in [[interval analysis]]
* ''double numbers'', [[Isaak Yaglom|I.M. Yaglom]] (1968), Kantor and Solodovnikov (1989), [[Michiel Hazewinkel|Hazewinkel]] (1990), Rooney (2014)
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