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Re: Python math is off by .000000000000045

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From Terry Reedy <tjreedy@udel.edu>
Subject Re: Python math is off by .000000000000045
Date Sun, 26 Feb 2012 00:44:08 -0500
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On 2/25/2012 9:49 PM, Devin Jeanpierre wrote:


> What this boils down to is to say that, basically by definition, the
> set of numbers representable in some finite number of binary digits is
> countable (just count up in binary value). But the whole of the real
> numbers are uncountable. The hard part is then accepting that some
> countable thing is 0% of an uncountable superset. I don't really know
> of any "proof" of that latter thing, it's something I've accepted
> axiomatically and then worked out backwards from there.

Informally, if the infinity of counts were some non-zero fraction f of 
the reals, then there would, in some sense, be 1/f times a many reals as 
counts, so the count could be expanded to count 1/f reals for each real 
counted before, and the reals would be countable. But Cantor showed that 
the reals are not countable.

But as you said, this is all irrelevant for computing. Since the number 
of finite strings is practically finite, so is the number of algorithms. 
And even a countable number of algorithms would be a fraction 0, for 
instance, of the uncountable predicate functions on 0, 1, 2, ... . So we 
do what we actually can that is of interest.

-- 
Terry Jan Reedy

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Thread

Python math is off by .000000000000045 Alec Taylor <alec.taylor6@gmail.com> - 2012-02-23 05:13 +1100
  Re: Python math is off by .000000000000045 nn <pruebauno@latinmail.com> - 2012-02-22 10:29 -0800
  Re: Python math is off by .000000000000045 Jussi Piitulainen <jpiitula@ling.helsinki.fi> - 2012-02-22 20:44 +0200
  Re: Python math is off by .000000000000045 Grant Edwards <invalid@invalid.invalid> - 2012-02-22 20:48 +0000
    Re: Python math is off by .000000000000045 Tobiah <toby@tobiah.org> - 2012-02-25 09:56 -0800
      Re: Python math is off by .000000000000045 Tim Wintle <tim.wintle@teamrubber.com> - 2012-02-25 19:08 +0000
      Re: Python math is off by .000000000000045 Terry Reedy <tjreedy@udel.edu> - 2012-02-25 16:05 -0500
        Re: Python math is off by .000000000000045 jmfauth <wxjmfauth@gmail.com> - 2012-02-25 13:25 -0800
          Re: Python math is off by .000000000000045 Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2012-02-25 22:51 +0000
            Re: Python math is off by .000000000000045 jmfauth <wxjmfauth@gmail.com> - 2012-02-26 01:59 -0800
              Re: Python math is off by .000000000000045 Ethan Furman <ethan@stoneleaf.us> - 2012-02-27 09:28 -0800
              Re: Python math is off by .000000000000045 Michael Torrie <torriem@gmail.com> - 2012-02-27 17:53 -0700
              Re: Python math is off by .000000000000045 Ethan Furman <ethan@stoneleaf.us> - 2012-02-28 09:56 -0800
      Re: Python math is off by .000000000000045 Devin Jeanpierre <jeanpierreda@gmail.com> - 2012-02-25 21:49 -0500
      Re: Python math is off by .000000000000045 Terry Reedy <tjreedy@udel.edu> - 2012-02-26 00:44 -0500
  Re: Python math is off by .000000000000045 John Ladasky <ladasky@my-deja.com> - 2012-02-26 16:24 -0800
    Re: Python math is off by .000000000000045 Terry Reedy <tjreedy@udel.edu> - 2012-02-26 20:30 -0500
    Re: Python math is off by .000000000000045 Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2012-02-27 03:28 +0000
      Re: Python math is off by .000000000000045 Grant Edwards <invalid@invalid.invalid> - 2012-02-27 15:02 +0000
        Re: Python math is off by .000000000000045 Michael Torrie <torriem@gmail.com> - 2012-02-27 08:34 -0700

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