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Re: What is precision of a number representation?

From Ben Finney <ben+python@benfinney.id.au>
Newsgroups comp.lang.python
Subject Re: What is precision of a number representation?
Date 2016-07-12 13:41 +1000
Message-ID <mailman.4.1468294936.21009.python-list@python.org> (permalink)
References (6 earlier) <5783c91e$0$1622$c3e8da3$5496439d@news.astraweb.com> <5783D63F.5040307@stoneleaf.us> <8560sbvqqd.fsf_-_@benfinney.id.au> <57840DFB.4000108@stoneleaf.us> <85y457ttdt.fsf@benfinney.id.au>

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Ethan Furman <ethan@stoneleaf.us> writes:

> On 07/11/2016 01:56 PM, Ben Finney wrote:
>
> > Precision is not a property of the number. It is a property of the
> > *representation* of that number.
> >
> > The representation “1×10²” has a precision of one digit.
> > The representation “100” has a precision of three digits.
> > The representation “00100” has a precision of five digits.
> > The representation “100.00” also has a precision of five digits.
>
> […] you haven't explained how 00100 is more precise than 100.

I haven't made any claim about “more precise” in the above.

But if you want such claims, here are comparable representations in
increasing order of precision:

* “0 ×10²” has one digit of precision.
* “0.0 ×10²” has two digits of precison.
* “0.01 ×10²” has three digits of precision.
* “0.010 ×10²” has four digits of precision.
* “0.0100 ×10²” has five digits of precision.
* “0.01000 ×10²” has six digits of precision.

Again, these might all be representations of the same number or of
different numbers; the representation claims only to represent a number
within a range of tolerance.


In decimal notation, some of the above can't be written with the same
precision. I could invent a representation — e.g. show “?” as a
place-holder for a digit not within the precision level. In that system,
the equivalent representations would be:

* “0????”
* “00???”
* “001??”
* “0010?”
* “00100”
* “00100.0”

Each of these claims to represent a quantity beginning at the
ten-thousands place, with increasing levels of precision in the claim.

So the comparison that invites is to show where the range of tolerance
for the representation ends. The fewer digits of precision, the less
precise the representation claims to be.

-- 
 \      “I find the whole business of religion profoundly interesting. |
  `\     But it does mystify me that otherwise intelligent people take |
_o__)                                    it seriously.” —Douglas Adams |
Ben Finney

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Curious Omission In New-Style Formats Lawrence D’Oliveiro <lawrencedo99@gmail.com> - 2016-07-09 22:54 -0700
  Re: Curious Omission In New-Style Formats Ian Kelly <ian.g.kelly@gmail.com> - 2016-07-10 01:21 -0600
    Re: Curious Omission In New-Style Formats Lawrence D’Oliveiro <lawrencedo99@gmail.com> - 2016-07-10 17:34 -0700
      Re: Curious Omission In New-Style Formats Ian Kelly <ian.g.kelly@gmail.com> - 2016-07-11 09:04 -0600
        Re: Curious Omission In New-Style Formats Steven D'Aprano <steve@pearwood.info> - 2016-07-12 02:28 +1000
          Re: Curious Omission In New-Style Formats Ethan Furman <ethan@stoneleaf.us> - 2016-07-11 10:24 -0700
            Re: Curious Omission In New-Style Formats Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2016-07-12 11:47 +1200
              Re: Curious Omission In New-Style Formats Ethan Furman <ethan@stoneleaf.us> - 2016-07-11 17:24 -0700
              Re: Curious Omission In New-Style Formats Ian Kelly <ian.g.kelly@gmail.com> - 2016-07-11 19:16 -0600
          Re: Curious Omission In New-Style Formats Ian Kelly <ian.g.kelly@gmail.com> - 2016-07-11 12:38 -0600
            Re: Curious Omission In New-Style Formats Steven D'Aprano <steve@pearwood.info> - 2016-07-12 13:38 +1000
              Re: Curious Omission In New-Style Formats Ian Kelly <ian.g.kelly@gmail.com> - 2016-07-13 00:21 -0600
                Re: Curious Omission In New-Style Formats Marko Rauhamaa <marko@pacujo.net> - 2016-07-13 09:57 +0300
                Re: Curious Omission In New-Style Formats Lawrence D’Oliveiro <lawrencedo99@gmail.com> - 2016-07-13 00:05 -0700
                Re: Curious Omission In New-Style Formats Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2016-07-13 18:49 +1000
                Re: Curious Omission In New-Style Formats Antoon Pardon <antoon.pardon@rece.vub.ac.be> - 2016-07-13 16:01 +0200
                Re: Curious Omission In New-Style Formats Dennis Lee Bieber <wlfraed@ix.netcom.com> - 2016-07-13 20:04 -0400
                Re: Curious Omission In New-Style Formats Lawrence D’Oliveiro <lawrencedo99@gmail.com> - 2016-07-13 15:24 -0700
                Re: Curious Omission In New-Style Formats Ian Kelly <ian.g.kelly@gmail.com> - 2016-07-13 18:45 -0600
                Re: Curious Omission In New-Style Formats Lawrence D’Oliveiro <lawrencedo99@gmail.com> - 2016-07-13 20:39 -0700
                Re: Curious Omission In New-Style Formats Ian Kelly <ian.g.kelly@gmail.com> - 2016-07-13 23:18 -0600
                Re: Curious Omission In New-Style Formats Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2016-07-14 17:47 +1000
                Re: Curious Omission In New-Style Formats Dennis Lee Bieber <wlfraed@ix.netcom.com> - 2016-07-14 07:34 -0400
                Re: Curious Omission In New-Style Formats Ian Kelly <ian.g.kelly@gmail.com> - 2016-07-14 08:30 -0600
                Re: Curious Omission In New-Style Formats Marko Rauhamaa <marko@pacujo.net> - 2016-07-14 19:02 +0300
                Re: Curious Omission In New-Style Formats Ian Kelly <ian.g.kelly@gmail.com> - 2016-07-14 11:10 -0600
                Re: Curious Omission In New-Style Formats Marko Rauhamaa <marko@pacujo.net> - 2016-07-14 20:30 +0300
                Re: Curious Omission In New-Style Formats Ian Kelly <ian.g.kelly@gmail.com> - 2016-07-14 18:17 -0600
                Re: Curious Omission In New-Style Formats Lawrence D’Oliveiro <lawrencedo99@gmail.com> - 2016-07-14 18:08 -0700
                Re: Curious Omission In New-Style Formats Marko Rauhamaa <marko@pacujo.net> - 2016-07-15 09:06 +0300
                Re: Curious Omission In New-Style Formats Antoon Pardon <antoon.pardon@rece.vub.ac.be> - 2016-07-15 09:54 +0200
                Re: Curious Omission In New-Style Formats Jussi Piitulainen <jussi.piitulainen@helsinki.fi> - 2016-07-15 11:40 +0300
                Re: Curious Omission In New-Style Formats Steven D'Aprano <steve@pearwood.info> - 2016-07-15 20:56 +1000
                Re: Curious Omission In New-Style Formats Antoon Pardon <antoon.pardon@rece.vub.ac.be> - 2016-07-15 13:44 +0200
                Re: Curious Omission In New-Style Formats Jussi Piitulainen <jussi.piitulainen@helsinki.fi> - 2016-07-15 16:38 +0300
                Re: Curious Omission In New-Style Formats Antoon Pardon <antoon.pardon@rece.vub.ac.be> - 2016-07-15 16:47 +0200
                Re: Curious Omission In New-Style Formats Jussi Piitulainen <jussi.piitulainen@helsinki.fi> - 2016-07-15 16:13 +0300
                Re: Curious Omission In New-Style Formats Steven D'Aprano <steve@pearwood.info> - 2016-07-16 01:12 +1000
                Re: Curious Omission In New-Style Formats Random832 <random832@fastmail.com> - 2016-07-15 09:39 -0400
                Re: Curious Omission In New-Style Formats Antoon Pardon <antoon.pardon@rece.vub.ac.be> - 2016-07-15 16:32 +0200
                Re: Curious Omission In New-Style Formats Antoon Pardon <antoon.pardon@rece.vub.ac.be> - 2016-07-15 13:05 +0200
                Re: Curious Omission In New-Style Formats Jussi Piitulainen <jussi.piitulainen@helsinki.fi> - 2016-07-15 16:28 +0300
                Re: Curious Omission In New-Style Formats Steven D'Aprano <steve@pearwood.info> - 2016-07-16 01:13 +1000
                Re: Curious Omission In New-Style Formats Jussi Piitulainen <jussi.piitulainen@helsinki.fi> - 2016-07-15 18:27 +0300
                Re: Curious Omission In New-Style Formats Marko Rauhamaa <marko@pacujo.net> - 2016-07-15 12:20 +0300
                Re: Curious Omission In New-Style Formats Antoon Pardon <antoon.pardon@rece.vub.ac.be> - 2016-07-15 12:44 +0200
                Re: Curious Omission In New-Style Formats Lawrence D’Oliveiro <lawrencedo99@gmail.com> - 2016-07-14 16:26 -0700
                Re: Curious Omission In New-Style Formats Robert Kern <robert.kern@gmail.com> - 2016-07-14 16:17 +0100
                Re: Curious Omission In New-Style Formats Lawrence D’Oliveiro <lawrencedo99@gmail.com> - 2016-07-15 16:35 -0700
                Re: Curious Omission In New-Style Formats Chris Angelico <rosuav@gmail.com> - 2016-07-16 10:57 +1000
                Re: Curious Omission In New-Style Formats MRAB <python@mrabarnett.plus.com> - 2016-07-14 01:59 +0100
              Re: Curious Omission In New-Style Formats Dennis Lee Bieber <wlfraed@ix.netcom.com> - 2016-07-13 07:46 -0400
                Re: Curious Omission In New-Style Formats Jussi Piitulainen <jussi.piitulainen@helsinki.fi> - 2016-07-13 16:04 +0300
              Re: Curious Omission In New-Style Formats Chris Angelico <rosuav@gmail.com> - 2016-07-13 23:00 +1000
                Re: Curious Omission In New-Style Formats Jussi Piitulainen <jussi.piitulainen@helsinki.fi> - 2016-07-13 16:16 +0300
                Re: Curious Omission In New-Style Formats Chris Angelico <rosuav@gmail.com> - 2016-07-13 23:49 +1000
                Re: Curious Omission In New-Style Formats Jussi Piitulainen <jussi.piitulainen@helsinki.fi> - 2016-07-13 17:23 +0300
                Re: Curious Omission In New-Style Formats Chris Angelico <rosuav@gmail.com> - 2016-07-14 00:28 +1000
          Re: Curious Omission In New-Style Formats Terry Reedy <tjreedy@udel.edu> - 2016-07-11 14:54 -0400
          Re: Curious Omission In New-Style Formats Ian Kelly <ian.g.kelly@gmail.com> - 2016-07-11 13:27 -0600
          Re: Curious Omission In New-Style Formats Michael Torrie <torriem@gmail.com> - 2016-07-11 14:06 -0600
          Re: Curious Omission In New-Style Formats Random832 <random832@fastmail.com> - 2016-07-11 16:34 -0400
          Re: Curious Omission In New-Style Formats Terry Reedy <tjreedy@udel.edu> - 2016-07-11 16:52 -0400
          What is precision of a number representation? (was: Curious Omission In New-Style Formats) Ben Finney <ben+python@benfinney.id.au> - 2016-07-12 06:56 +1000
            Re: What is precision of a number representation? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2016-07-11 23:28 +0100
          Re: What is precision of a number representation? Ethan Furman <ethan@stoneleaf.us> - 2016-07-11 14:22 -0700
          Re: What is precision of a number representation? (was: Curious Omission In New-Style Formats) Chris Angelico <rosuav@gmail.com> - 2016-07-12 07:51 +1000
            Re: What is precision of a number representation? (was: Curious Omission In New-Style Formats) Jan Coombs <jenfhaomndgfwutc@murmic.plus.com> - 2016-07-12 00:14 +0100
              Re: What is precision of a number representation? (was: Curious Omission In New-Style Formats) Chris Angelico <rosuav@gmail.com> - 2016-07-12 09:57 +1000
            Re: What is precision of a number representation? (was: Curious Omission In New-Style Formats) Steven D'Aprano <steve@pearwood.info> - 2016-07-12 14:19 +1000
              Re: What is precision of a number representation? (was: Curious Omission In New-Style Formats) Chris Angelico <rosuav@gmail.com> - 2016-07-12 14:36 +1000
              Re: What is precision of a number representation? Antoon Pardon <antoon.pardon@rece.vub.ac.be> - 2016-07-12 11:50 +0200
                Re: What is precision of a number representation? Marko Rauhamaa <marko@pacujo.net> - 2016-07-12 13:27 +0300
                Re: What is precision of a number representation? Antoon Pardon <antoon.pardon@rece.vub.ac.be> - 2016-07-12 13:02 +0200
                Re: What is precision of a number representation? Steven D'Aprano <steve@pearwood.info> - 2016-07-12 23:16 +1000
          Re: What is precision of a number representation? Ethan Furman <ethan@stoneleaf.us> - 2016-07-11 15:17 -0700
            Re: What is precision of a number representation? Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2016-07-12 16:21 +1000
              Re: What is precision of a number representation? Random832 <random832@fastmail.com> - 2016-07-12 09:36 -0400
          Re: What is precision of a number representation? Ethan Furman <ethan@stoneleaf.us> - 2016-07-11 15:29 -0700
          Re: Curious Omission In New-Style Formats Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2016-07-12 11:26 +1200
          Re: What is precision of a number representation? Chris Angelico <rosuav@gmail.com> - 2016-07-12 11:57 +1000
          Re: What is precision of a number representation? Ben Finney <ben+python@benfinney.id.au> - 2016-07-12 13:41 +1000
          Re: What is precision of a number representation? Terry Reedy <tjreedy@udel.edu> - 2016-07-12 00:14 -0400
          Re: What is precision of a number representation? Terry Reedy <tjreedy@udel.edu> - 2016-07-12 00:17 -0400

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