On Fri, 25 Aug 2017 02:21 pm, Chris Angelico wrote:
> In fact, the ONLY way to create this confusion is to use (some
> derivative of) one fifth, which is a factor of base 10 but not of base
> 2. Any other fraction will either terminate in both bases (eg "0.125"
> in decimal or "0.001" in binary), or repeat in both (any denominator
> with any other prime number in it). No other rational numbers can
> produce this apparently-irrational behaviour, pun intended.
I think that's a bit strong. A lot strong. Let's take 1/13 for example:
py> from decimal import Decimal
py> sum([1/13]*13)
0.9999999999999998
py> sum([Decimal(1)/Decimal(13)]*13)
Decimal('0.9999999999999999999999999997')
Or 2/7, added 7 times, should be 2:
py> sum([2/7]*7)
1.9999999999999996
py> sum([Decimal(2)/Decimal(7)]*7)
Decimal('2.000000000000000000000000001')
Its not just addition that "fails". We can take the reciprocal of the reciprocal
of a number, and expect to get the original number:
py> 1/(1/99)
98.99999999999999
py> Decimal(1)/( Decimal(1)/Decimal(99) )
Decimal('99.00000000000000000000000001')
or we can multiply a fraction by the denominator and expect to get the
numerator:
py> (7/207)*207
6.999999999999999
py> (Decimal(7)/Decimal(207))*Decimal(207)
Decimal('6.999999999999999999999999999')
These are not isolated examples.
You'll note that none of the numbers involved are multiples of 5.
Besides: the derivative of 1/5 is 0, like that of every other constant.
*wink*
--
Steve
“Cheer up,” they said, “things could be worse.” So I cheered up, and sure
enough, things got worse.
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