Re: More on trits & tetrits... (long)
(Context: implications of Exact and Inexact Zeros and Infinities)
Replying to John Pryce, Vincent Lefèvre wrote:
> > If we go on in this way we might produce the Nonstandard Reals with
> > infinitely many infinities and infinitesimals...
>
> I think this would go too far. Ditto for the 5th infinity: only 3 are
> necessary for floating-point (1 / exact 0 should be NaN, as this isn't
> defined over the real numbers).
That would be a very different arithmetic. Yes, 1788 is defined over
the Reals, but 754 is defined over the Affine Extended Reals, which is
also why it has signed zeros as well as signed infinities.
Michel.
---Sent: 2010-04-28 16:08:58 UTC