4 ms·
Is any number mod infinity equal to itself?
by api 4y ago
Is any number mod infinity equal to itself?
- tromp 4y agoIn the surreal numbers [1], the definition of division and hence modulo applies to all numbers, finite and infinite alike. And for any finite number -omega < x < omega you would indeed have x mod omega == x. [1] https://en.wikipedia.org/wiki/Surreal_number https://en.wikipedia.org/wiki/Surreal_number
- SAI_Peregrinus 4y agoYou might already know about it, but Ehrlich claims[1] that the Surreals form an ordered field which is a maximal hyperreal number system in NBG, and therefore all the results of non-standard analysis "work" (up to isomorphism) in the Surreals. [1] Philip Ehrlich. "The absolute arithmetic continuum and the unification of all numbers great and small." Bull. Symbolic Logic 18 (1) 1 - 45, March 2012. https://doi.org/10.2178/bsl/1327328438 https://doi.org/10.2178/bsl/1327328438 Theorem 20
- gspr 4y agoWhat do you want mod infinity to mean?