Abstract
The notions of hyperfinite approximations of locally compact groups and of the field of reals are introduced. It is proved that the groups, which are approximated by hyperfinite groups are unimodular, but this condition is not sufficient — the group SO(3) is not approximable by hyperfinite groups.
The algebraic systems, which approximate R are the hyperfinite versions of computer arithmetics implemented in existing computers. The nonapproximability of some matrix groups implies the impossibility to approximate R by a hyperfinite field in a such way that the operation of taking an inverse element in R is approximated by the similar operation in approximating hyperfinite field.
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References
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© 2001 Springer Science+Business Media Dordrecht
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Gordon, E.I., Rezvova, O.A. (2001). On Hyperfinite Approximations of the Field R . In: Schuster, P., Berger, U., Osswald, H. (eds) Reuniting the Antipodes — Constructive and Nonstandard Views of the Continuum. Synthese Library, vol 306. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9757-9_8
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DOI: https://doi.org/10.1007/978-94-015-9757-9_8
Publisher Name: Springer, Dordrecht
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