Lie Lie.1296 at gmail.com
Tue Feb 26 12:50:40 CET 2008

```On Feb 25, 5:41 am, Steven D'Aprano <st... at REMOVE-THIS-
cybersource.com.au> wrote:
> On Sun, 24 Feb 2008 10:09:37 -0800, Lie wrote:
> > 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.
>
> *jaw drops*
>
> Please stop trying to "help" convince people that rational classes are
> safe to use. That's the sort of "help" that we don't need.
>
> For the record, it is a perfectly good strategy to *artificially* limit
> the denominator of fractions to some maximum value. (That's more or less
> the equivalent of setting your floating point values to a maximum number
> of decimal places.) But without that artificial limit, repeated addition
> of fractions risks having the denominator increase without limit.
>
> --
> Steven

No, it is a real limit. This is what I'm talking about. If the input
data has a limit, the output data has a real limit, not a defined-
limit. If the input data's denominator is unbounded, the output
fraction's denominator is also unbounded

In a repeated addition and subtraction with input data that have limits

```