Lie Lie.1296 at gmail.com
Sun Feb 24 19:09:37 CET 2008

```On Feb 25, 12:46 am, Steve Holden <st... at holdenweb.com> wrote:
> Lie wrote:
> > On Feb 18, 1:25 pm, Carl Banks <pavlovevide... at gmail.com> wrote:
> >> On Feb 17, 1:45 pm, Lie <Lie.1... at gmail.com> wrote:
>
> >>>> Any iteration with repeated divisions and additions can thus run the
> >>>> denominators up.  This sort of calculation is pretty common (examples:
> >>>> compound interest, numerical integration).
> >>> Wrong. Addition and subtraction would only grow the denominator up to
> >>> a certain limit
> >> I said repeated additions and divisions.
>
> > Repeated Addition and subtraction can't make fractions grow
> > infinitely, only multiplication and division could.
>
> On what basis is this claim made?
>
> (n1/d1) + (n2/d2) = ((n1*d2) + (n2*d1)) / (d1*d2)
>
> If d1 and d2 are mutually prime (have no common factors) then it is
> impossible to reduce the resulting fraction further in the general case
> (where n1 = n2 = 1, for example).
>
> >> Anyways, addition and subtraction can increase the denominator a lot
> >> if for some reason you are inputing numbers with many different
> >> denominators.
>
> > Up to a certain limit. After you reached the limit, the fraction would
> > always be simplifyable.
>
> Where does this magical "limit" appear from?
>
> > If the input numerator and denominator have a defined limit, repeated
> > addition and subtraction to another fraction will also have a defined
> > limit.
>
> Well I suppose is you limit the input denominators to n then you have a
> guarantee that the output denominators won't exceed n!, but that seems
> like a pretty poor guarantee to me.
>
> Am I wrong here? You seem to be putting out unsupportable assertions.
> Please justify them or stop making them.
>

Well, I do a test on my own fraction class. I found out that if we set
a limit to the numerators and denominators, the resulting output
fraction would have limit too. I can't grow my fraction any more than
this limit no matter how many iteration I do on them. I do the test is
by something like this (I don't have the source code with me right
now, it's quite long if it includes the fraction class, but I think
you could use any fraction class that automatically simplify itself,
might post the real code some time later):

while True:
a = randomly do (a + b) or (a - b)
b = random fraction between [0-100]/[0-100]
print a

And this limit is much lower than n!. I think it's sum(primes(n)), but
I've got no proof for this one yet.

```