Re: Rational Numbers/Irrational Numbers

dta@xxxxxxxx wrote:


1/1, 1/2, 2/1, 3/1, 2/2, 1/3, 1/4, 2/3, ...

I'm not seeing the algorithm behind the sequence above. Could you
state it explicitly?

The concept I understand (the mapping), just I don't see how the
sequence above is generated.

It's not really an "algorithm" but an ordering. The ordering
is given, on the set of (positive) rational numbers in reduced
form h/k with (h,k)=1) by declaring that h1/k1 preceeds h2/k2
if h1+k1 < h2+k2. In the case h1+k1 = h2+k2,then we declare
that h1/k1 preceeds h2/k2 if h1<h2.

In other words, we first sort first on the sum of the numerator
and denominator and then sort by numerators. (This is taken
from Ivan Niven's monograph.)

Bart

--
The man without a .sig
.

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