In this chapter we introduce real hypernumbers and study their properties in Sect. 2.1. Algebraic properties are explored in Sect. 2.2, and topological properties are investigated in Sect. 2.3. In a similar way, it is possible to build complex hypernumbers and study their properties (Burgin 2002, 2004, 2010).
- Borel, E.: Les Nombre Inaccessible. Gauthier-Villiars, Paris (1952)Google Scholar
- Burgin, M.: Hypermeasures and hyperintegration. Not. Nat. Acad. Sci. Ukr. (in Russian and Ukrainian) 6, 10–13 (1990)Google Scholar
- Burgin, M.: Extrafunctions, distributions, and nonsmooth analysis. Mathematics Report Series, MRS Report. 1 Feb 2001, p. 47. University of California, Los Angeles (2001)Google Scholar
- Burgin, M.: Hyperfunctionals and generalized distributions. In: Krinik, A.C., Swift, R.J. (eds.) Stochastic processes and functional analysis, a Dekker series of lecture notes in pure and applied mathematics, vol. 238, pp. 81–119. CRC Press, Boca Raton, FL (2004)Google Scholar
- Kurosh, A.G.: Lectures on general algebra. Chelsea P. C, New York (1963)Google Scholar
- Ross, K.A.: Elementary analysis: the theory of calculus. Springer, New York (1996)Google Scholar