Re: lojban as a programming language [was Re: [lojban] Lojban for lay programmers]

[John Cowan <cowan@ccil.org>]

Jim Carter scripsit:

> In 64 bit IEEE float, let X = 1; Y = 1e-17 (and the LSB is about 2e-16).
> If IEEE floats were closed under addition, the "first law" for groups, then
> X+Y has to have a IEEE representation.  Let Z = X+Y.  But Z == 1; the sum
> is truncated on the right to 56 bits.  So we've just proved that Y == 0,
> because 0 is the group member (provably unique) such that W + 0 == W for
> every W in the group.  Oops.

Ah, but just because X + Y = X for some X, Y does not make Y the
zero; for that to work, X + Y has to = X for *every* X.

-- 
John Cowan           http://www.ccil.org/~cowan              cowan@ccil.org
Please leave your values        |       Check your assumptions.  In fact,
   at the front desk.           |          check your assumptions at the door.
     --sign in Paris hotel      |            --Miles Vorkosigan