"Grant Edwards" <[EMAIL PROTECTED]> wrote in message news:[EMAIL PROTECTED] > On 2006-05-08, Thomas Bartkus <[EMAIL PROTECTED]> wrote: > > >> does python support true rations, which means that 1/3 is a > >> true one-third and not 0.333333333 rounded off at some > >> arbitrary precision? > > > > At risk of being boring ;-) > > > > - Python supports both rational and irrational numbers as > > floating point numbers the way any language on any digital > > computer does - imprecisely. > > > > A "true" (1/3) can only be expressed as a fraction. > > At the risk of being both boring and overly pedantic, that's > not true. In base 3, the value in question is precisely > representable in floating point: 0.1 > > > As soon as you express it as a floating point - you are in a > > bit of trouble because that's impossible. > > It's not possible in base 2 or base 10. It's perfectly > possible in base 9 (used by the Nenets of Northern Russia) base > 12 (popular on planets where everybody has twelve toes) or base > 60 (used by th Sumerians). [I don't know if any of those > peoples used floating point in those bases -- I'm just pointing > out that your prejudice towards base 10 notation is showing.] > > > You can not express (1/3) as a floating point in Python any > > more than you can do it with pencil and paper. > > That's true assuming base 2 in Python and base 10 on paper. The > base used by Python is pretty much etched in stone (silicon, to > be precise). There used to be articles about people working on > base-3 logic gates, but base-3 logic never made it out of the > lab. However, you can pick any base you want when using paper > and pencil. > > > You can be precise and write "1/3" or you can surrender to > > arithmetic convenience and settle for the imprecise by writing > > "0.333333333", chopping it off at some arbitrary precision. > > Or you can write 0.1 > 3 > > :)
Ahhh! But if I need to store the value 1/10 (decimal!), what kind of a precision pickle will I then find myself while working in base 3 ? How much better for precision if we just learn our fractions and stick to storing integer numerators alongside integer denominators in big 128 bit double registers ? Even the Nenets might become more computationally precise by such means ;-) And how does a human culture come to decide on base 9 arithmetic anyway? Even base 60 makes more sense if you like it when a lot of divisions come out nice and even. Do the Nenets amputate the left pinky as a rite of adulthood ;-) Thomas Bartkus -- http://mail.python.org/mailman/listinfo/python-list
