Re: Clean Object Class Design -- Circle/Ellipse

Vadim Tropashko wrote:
> In article <7MUb7.1661$NJ6.5968_at_www.newsranger.com>, Mikito Harakiri says...
> >
> >>Well, let's see, it should hold for all Reals x, y that,
> >>
> >> floor(x) I+ floor(y) = floor(x R+ y)
> >>
> >>Yes, it holds, so they could, if this is your only operator. :-)
> >
> >You mean '+' is my only operator? I see that I can't make it
> >
> >floor(x) I* floor(y) <==> floor(x R* y)
> >
> It doesn't hold for '+' either.
>
> floor(1.9) I+ floor(1.9) = 2
>
> while
>
> floor(1.9+1.9) = 3

Oh dear, you are right. Thanks for the correction. It also does not work for round():

  round(1.5) I+ round(1.5) = 4, but

  round(1.5 R+ 1.5) = 3

In fact, it can be shown that such a mapping cannot exist. It holds that the mapping maps the integer Reals to the corresponding Integer and it should also hold that

  f(1/2) I+ f(1/2) = f(1/2 R+ 1/2) = f(1) = 1.

So f(1/2) should be an integer x such that x + x = 1.

-- 
  Jan Hidders