On Tue, 29 Sep 2009 01:18:43 pm Guido van Rossum wrote:
I've never heard of someone who had a use case for
denormalized fractions
Off-topic, but for what it's worth, I have one -- there's a mathematical
operator called the mediant:
mediant(a/b, c/d) = (a+c)/(b+d)
It has a few uses, including Farey fractions. Clearly the result you get
from normalized fractions will be different from denormalized (compare
mediant(1/2, 3/4) with mediant(5/10, 3/4)). This leads to Simpson's
Paradox, which is of importance in medical research:
http://en.wikipedia.org/wiki/Simpson's_paradox
Brief summary: consider two medical studies comparing two different
treatments for an illness, treatment A and B. According to the first
study, treatment A is better; according to the second study, treatment
A is also better. But combining the results of the two studies into a
single comparison paradoxically shows that treatment B is better!
The mediant is fascinating (to maths geeks at least) and important, and
you need denormalized fractions.
--
Steven D'Aprano
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