HaloO, I wrote:
That is you can do the usual Int arithmetic in the ranges Inf..^Inf*2 and -Inf*2^..-Inf except that Inf has no predecessor and -Inf no successor. Well, and we lose commutativity of + and *. I.e. 1 + $a != $a + 1 if $a is transfinite.
Well, we can of course count downwards from Inf to Inf-1, Inf-2, etc. That is we don't have a global sign but signed coefficients with the highest multiple of Inf determining the side of Zero we are on. For the Num type we also might consider reciprocals of Inf as infinitesimals. The only thing we need to define then is at which points in computations these hypernums are standardized back into Num ;) An application for transfinite Ints is if you have two "infinite" files concatenated into one. Then you can keep transfinite indices into the second one. The size of such a file would be Inf*2 of course. Regards, TSa. -- "The unavoidable price of reliability is simplicity" -- C.A.R. Hoare "Simplicity does not precede complexity, but follows it." -- A.J. Perlis 1 + 2 + 3 + 4 + ... = -1/12 -- Srinivasa Ramanujan
