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Re: Should non-security 2.7 bugs be fixed?

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  Re: Should non-security 2.7 bugs be fixed? Devin Jeanpierre <jeanpierreda@gmail.com> - 2015-07-18 19:33 -0700
    Re: Should non-security 2.7 bugs be fixed? Rick Johnson <rantingrickjohnson@gmail.com> - 2015-07-18 19:49 -0700
    Re: Should non-security 2.7 bugs be fixed? Rustom Mody <rustompmody@gmail.com> - 2015-07-18 20:52 -0700
      Re: Should non-security 2.7 bugs be fixed? Rick Johnson <rantingrickjohnson@gmail.com> - 2015-07-18 21:18 -0700
      Devanagari int literals [was Re: Should non-security 2.7 bugs be fixed?] Steven D'Aprano <steve@pearwood.info> - 2015-07-19 14:45 +1000
        Re: Devanagari int literals [was Re: Should non-security 2.7 bugs be fixed?] Chris Angelico <rosuav@gmail.com> - 2015-07-19 15:06 +1000
          Re: Devanagari int literals [was Re: Should non-security 2.7 bugs be fixed?] Marko Rauhamaa <marko@pacujo.net> - 2015-07-19 10:16 +0300
            Re: Devanagari int literals [was Re: Should non-security 2.7 bugs be fixed?] Rustom Mody <rustompmody@gmail.com> - 2015-07-19 00:32 -0700
              Re: Devanagari int literals [was Re: Should non-security 2.7 bugs be fixed?] Marko Rauhamaa <marko@pacujo.net> - 2015-07-19 10:44 +0300
              Re: Devanagari int literals [was Re: Should non-security 2.7 bugs be fixed?] Terry Reedy <tjreedy@udel.edu> - 2015-07-19 19:13 -0400
                Re: Devanagari int literals [was Re: Should non-security 2.7 bugs be fixed?] Rustom Mody <rustompmody@gmail.com> - 2015-07-19 19:02 -0700
        Re: Devanagari int literals [was Re: Should non-security 2.7 bugs be fixed?] Anuradha Laxminarayan <lanuradha@gmail.com> - 2015-07-18 23:25 -0700
        Re: Devanagari int literals [was Re: Should non-security 2.7 bugs be fixed?] Terry Reedy <tjreedy@udel.edu> - 2015-07-19 04:26 -0400
        Re: Devanagari int literals [was Re: Should non-security 2.7 bugs be fixed?] Tim Chase <python.list@tim.thechases.com> - 2015-07-19 07:56 -0500
        Re: Devanagari int literals [was Re: Should non-security 2.7 bugs be fixed?] Chris Angelico <rosuav@gmail.com> - 2015-07-20 04:07 +1000
        Re: Devanagari int literals [was Re: Should non-security 2.7 bugs be fixed?] Tim Chase <python.list@tim.thechases.com> - 2015-07-19 14:55 -0500
        Re: Devanagari int literals [was Re: Should non-security 2.7 bugs be fixed?] Chris Angelico <rosuav@gmail.com> - 2015-07-20 07:16 +1000
          Re: Devanagari int literals [was Re: Should non-security 2.7 bugs be fixed?] wxjmfauth@gmail.com - 2015-07-20 00:43 -0700
        Re: Devanagari int literals [was Re: Should non-security 2.7 bugs be fixed?] MRAB <python@mrabarnett.plus.com> - 2015-07-19 23:13 +0100
        Re: Devanagari int literals [was Re: Should non-security 2.7 bugs be fixed?] Rustom Mody <rustompmody@gmail.com> - 2015-07-20 20:30 -0700
          Re: Devanagari int literals [was Re: Should non-security 2.7 bugs be fixed?] Chris Angelico <rosuav@gmail.com> - 2015-07-21 13:43 +1000
            Re: Devanagari int literals [was Re: Should non-security 2.7 bugs be fixed?] Rustom Mody <rustompmody@gmail.com> - 2015-07-20 23:11 -0700
          Re: Devanagari int literals [was Re: Should non-security 2.7 bugs be fixed?] Laura Creighton <lac@openend.se> - 2015-07-21 10:10 +0200
            Re: Devanagari int literals [was Re: Should non-security 2.7 bugs be fixed?] Marko Rauhamaa <marko@pacujo.net> - 2015-07-21 12:10 +0300
              Re: Devanagari int literals [was Re: Should non-security 2.7 bugs be fixed?] Chris Angelico <rosuav@gmail.com> - 2015-07-21 19:18 +1000
                Re: Devanagari int literals [was Re: Should non-security 2.7 bugs be fixed?] Marko Rauhamaa <marko@pacujo.net> - 2015-07-21 13:13 +0300
              Re: Devanagari int literals [was Re: Should non-security 2.7 bugs be fixed?] Mark Lawrence <breamoreboy@yahoo.co.uk> - 2015-07-21 11:34 +0100
              Re: Devanagari int literals [was Re: Should non-security 2.7 bugs be fixed?] Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-07-21 20:39 +1000
                Re: Devanagari int literals [was Re: Should non-security 2.7 bugs be fixed?] Marko Rauhamaa <marko@pacujo.net> - 2015-07-21 13:54 +0300
                  Re: Devanagari int literals [was Re: Should non-security 2.7 bugs be fixed?] Marko Rauhamaa <marko@pacujo.net> - 2015-08-09 00:27 +0300
                    Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?] Rustom Mody <rustompmody@gmail.com> - 2015-08-09 09:29 -0700
                Re:  Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?] Rustom Mody <rustompmody@gmail.com> - 2015-07-22 06:34 -0700
                  OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?] Steven D'Aprano <steve@pearwood.info> - 2015-07-23 02:58 +1000
                    Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?] Laura Creighton <lac@openend.se> - 2015-07-22 19:17 +0200
                      Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?] Rustom Mody <rustompmody@gmail.com> - 2015-07-22 10:49 -0700
                        Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?] Laura Creighton <lac@openend.se> - 2015-07-22 20:14 +0200
                        Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?] Mark Lawrence <breamoreboy@yahoo.co.uk> - 2015-07-22 21:59 +0100
                    Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?] Steven D'Aprano <steve@pearwood.info> - 2015-07-23 03:21 +1000
                      Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?] Dennis Lee Bieber <wlfraed@ix.netcom.com> - 2015-07-22 21:44 -0400
                      Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?] Chris Angelico <rosuav@gmail.com> - 2015-07-23 12:00 +1000
                    Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?] Paul Rubin <no.email@nospam.invalid> - 2015-07-22 10:48 -0700
                      Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?] Rustom Mody <rustompmody@gmail.com> - 2015-07-22 10:51 -0700
                      Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?] Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-07-23 15:14 +1000
                    Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?] Rustom Mody <rustompmody@gmail.com> - 2015-07-22 11:09 -0700
                      Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?] Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-07-23 15:41 +1000
                        Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?] Marko Rauhamaa <marko@pacujo.net> - 2015-07-23 23:59 +0300
                          Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?] Chris Angelico <rosuav@gmail.com> - 2015-07-24 07:03 +1000
                            Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?] Marko Rauhamaa <marko@pacujo.net> - 2015-07-24 00:29 +0300
                              Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?] Mark Lawrence <breamoreboy@yahoo.co.uk> - 2015-07-23 22:50 +0100
                              Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?] Laura Creighton <lac@openend.se> - 2015-07-23 23:52 +0200
                                Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?] Marko Rauhamaa <marko@pacujo.net> - 2015-07-24 00:59 +0300
                                  Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?] Chris Angelico <rosuav@gmail.com> - 2015-07-24 08:02 +1000
                              Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?] Chris Angelico <rosuav@gmail.com> - 2015-07-24 08:00 +1000
                              Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?] MRAB <python@mrabarnett.plus.com> - 2015-07-23 23:01 +0100
                              Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?] Laura Creighton <lac@openend.se> - 2015-07-24 00:19 +0200
                              Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?] Mark Lawrence <breamoreboy@yahoo.co.uk> - 2015-07-23 23:56 +0100
                              Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?] Grant Edwards <invalid@invalid.invalid> - 2015-07-24 00:07 +0000
                                Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?] Rick Johnson <rantingrickjohnson@gmail.com> - 2015-07-23 18:40 -0700
                                Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?] Paul Rubin <no.email@nospam.invalid> - 2015-07-23 19:03 -0700
                                  Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?] Rick Johnson <rantingrickjohnson@gmail.com> - 2015-07-23 20:16 -0700
                                  Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?] Grant Edwards <invalid@invalid.invalid> - 2015-07-24 14:13 +0000
                                    Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?] Paul Rubin <no.email@nospam.invalid> - 2015-07-24 08:45 -0700
                                    Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?] Mark Lawrence <breamoreboy@yahoo.co.uk> - 2015-07-24 16:58 +0100
                              Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?] Rustom Mody <rustompmody@gmail.com> - 2015-07-23 22:15 -0700
                      Re: OT Re: Math-embarrassment results in CS [was: Should non-security   2.7 bugs be fixed?] Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2015-07-23 18:57 +1200
                        Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?] Rustom Mody <rustompmody@gmail.com> - 2015-07-23 02:12 -0700
                        Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?] Rustom Mody <rustompmody@gmail.com> - 2015-07-23 05:52 -0700
                    Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?] Marko Rauhamaa <marko@pacujo.net> - 2015-07-23 11:24 +0300
          Re: Devanagari int literals [was Re: Should non-security 2.7 bugs be fixed?] Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-07-21 18:57 +1000
      Re: Should non-security 2.7 bugs be fixed? Terry Reedy <tjreedy@udel.edu> - 2015-07-19 02:44 -0400
      Re: Should non-security 2.7 bugs be fixed? Terry Reedy <tjreedy@udel.edu> - 2015-07-19 05:11 -0400
        Re: Should non-security 2.7 bugs be fixed? Rustom Mody <rustompmody@gmail.com> - 2015-07-19 07:30 -0700
      Re: Should non-security 2.7 bugs be fixed? Mark Lawrence <breamoreboy@yahoo.co.uk> - 2015-07-19 15:00 +0100
    Re: Should non-security 2.7 bugs be fixed? Steven D'Aprano <steve@pearwood.info> - 2015-07-19 14:45 +1000
      Re: Should non-security 2.7 bugs be fixed? Devin Jeanpierre <jeanpierreda@gmail.com> - 2015-07-19 18:20 -0700
        Re: Should non-security 2.7 bugs be fixed? Steven D'Aprano <steve@pearwood.info> - 2015-07-20 13:05 +1000
          Re: Should non-security 2.7 bugs be fixed? Devin Jeanpierre <jeanpierreda@gmail.com> - 2015-07-19 20:41 -0700
      Re: Should non-security 2.7 bugs be fixed? Mark Lawrence <breamoreboy@yahoo.co.uk> - 2015-07-20 02:46 +0100
        Re: Should non-security 2.7 bugs be fixed? Rustom Mody <rustompmody@gmail.com> - 2015-07-19 19:16 -0700
          Re: Should non-security 2.7 bugs be fixed? Chris Angelico <rosuav@gmail.com> - 2015-07-20 12:59 +1000
          Re: Should non-security 2.7 bugs be fixed? Mark Lawrence <breamoreboy@yahoo.co.uk> - 2015-07-20 11:59 +0100
          Re: Should non-security 2.7 bugs be fixed? Rick Johnson <rantingrickjohnson@gmail.com> - 2015-07-20 20:04 -0700
            Re: Should non-security 2.7 bugs be fixed? Rustom Mody <rustompmody@gmail.com> - 2015-07-20 20:15 -0700
              Re: Should non-security 2.7 bugs be fixed? Chris Angelico <rosuav@gmail.com> - 2015-07-21 13:33 +1000
              Re: Should non-security 2.7 bugs be fixed? Terry Reedy <tjreedy@udel.edu> - 2015-07-21 00:45 -0400
            Re: Should non-security 2.7 bugs be fixed? breamoreboy@gmail.com - 2015-07-21 14:22 -0700
              Re: Should non-security 2.7 bugs be fixed? Rick Johnson <rantingrickjohnson@gmail.com> - 2015-07-21 19:07 -0700
                Re: Should non-security 2.7 bugs be fixed? Terry Reedy <tjreedy@udel.edu> - 2015-07-22 02:51 -0400
                  Re: Should non-security 2.7 bugs be fixed? Rick Johnson <rantingrickjohnson@gmail.com> - 2015-07-22 16:37 -0700
      Re: Should non-security 2.7 bugs be fixed? Terry Reedy <tjreedy@udel.edu> - 2015-07-20 02:25 -0400
      Re: Should non-security 2.7 bugs be fixed? dieter <dieter@handshake.de> - 2015-07-20 08:58 +0200
      Re: Should non-security 2.7 bugs be fixed? Devin Jeanpierre <jeanpierreda@gmail.com> - 2015-07-20 00:13 -0700

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#94264 — Re: Devanagari int literals [was Re: Should non-security 2.7 bugs be fixed?]

On Tue, Jul 21, 2015 at 1:30 PM, Rustom Mody <rustompmody@gmail.com> wrote:
> BTW my boys have just mailed me their latest:
>
>>>> 九.九九
>
> 9.99
>
> Can some unicode/Chinese literate person inform me whether
> that ideograph is equivalent to roman '9' or roman 'nine'?

I'm not Chinese-literate, but I know how to dig up info from the
Unicode side of things.

'\u4e5d' CJK UNIFIED IDEOGRAPH-4E5D

Thanks, very helpful.

Perhaps slightly more useful:

https://en.wiktionary.org/wiki/%E4%B9%9D

But it still doesn't disambiguate digit vs word.

Playing around with Google Translate suggests that it functions mostly
like a digit; 九九 means "Ninety-nine" and 九八 means "Ninety-eight". But
I'll leave further confirmation to someone who fits your second
description.

ChrisA

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#94272 — Re: Devanagari int literals [was Re: Should non-security 2.7 bugs be fixed?]

On Tuesday, July 21, 2015 at 9:13:49 AM UTC+5:30, Chris Angelico wrote:
> On Tue, Jul 21, 2015 at 1:30 PM, Rustom Mody wrote:
> > BTW my boys have just mailed me their latest:
> >
> >>>> 九.九九
> >
> > 9.99
> >
> > Can some unicode/Chinese literate person inform me whether
> > that ideograph is equivalent to roman '9' or roman 'nine'?
> 
> I'm not Chinese-literate, but I know how to dig up info from the
> Unicode side of things.
> 
> '\u4e5d' CJK UNIFIED IDEOGRAPH-4E5D
> 
> Thanks, very helpful.
> 
> Perhaps slightly more useful:
> 
> https://en.wiktionary.org/wiki/%E4%B9%9D
> 
> But it still doesn't disambiguate digit vs word.
> 
> Playing around with Google Translate suggests that it functions mostly
> like a digit; 九九 means "Ninety-nine" and 九八 means "Ninety-eight". But
> I'll leave further confirmation to someone who fits your second
> description.
> 
> ChrisA

Well Cant make much sense of it:

>>> import unicodedata as ud
>>> ud.numeric('२')
2.0
>>> ud.category('२')
'Nd'
>>> ud.numeric('九')
9.0
>>> ud.category('九')
'Lo'
>>> 

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#94274 — Re: Devanagari int literals [was Re: Should non-security 2.7 bugs be fixed?]

In a message of Mon, 20 Jul 2015 20:30:48 -0700, Rustom Mody writes:

>BTW my boys have just mailed me their latest:
>
>>>> 九.九九
>                                                                            
>9.99
>
>Can some unicode/Chinese literate person inform me whether
>that ideograph is equivalent to roman '9' or roman 'nine'?

Ah, I don't understand you.  What do you mean roman 'nine'?  a
phonetic way of saying things?  What bankers use to help prevent
forgeries? Something else?

九 is a numberal.  The numberal 9.  For absolutely certain.  But since
I don't know what you mean by 'nine' it may mean that, as well.  九 is
not restricted to any particular dialect of Chinese -- if you speak
any chinese you will know what this means.  On the other hand the
pinyan (phonetic) way to pronounce numbers can vary between dialects.

Chinese has *many* ways of writing numbers, at least 4 I know about.
See: https://en.wikipedia.org/wiki/Chinese_numerals

Laura

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#94279 — Re: Devanagari int literals [was Re: Should non-security 2.7 bugs be fixed?]

Laura Creighton <lac@openend.se>:

> In a message of Mon, 20 Jul 2015 20:30:48 -0700, Rustom Mody writes:
>
>>Can some unicode/Chinese literate person inform me whether that
>>ideograph is equivalent to roman '9' or roman 'nine'?
>
> Ah, I don't understand you. What do you mean roman 'nine'? a phonetic
> way of saying things? What bankers use to help prevent forgeries?
> Something else?

This is getting deep. It is an embarrassing metamathematical fact that
numbers cannot be defined. At least, mathematicians gave up trying a
century ago.

   In mathematics, the essence of counting a set and finding a result n,
   is that it establishes a one to one correspondence (or bijection) of
   the set with the set of numbers {1, 2, ..., n}.
   <URL: https://en.wikipedia.org/wiki/Counting#Counting_in_mathematics>

Our ancestors defined the fingers (or digits) as "the set of numbers."
Modern mathematicians have managed to enhance the definition
quantitatively but not qualitatively.


Marko

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#94280 — Re: Devanagari int literals [was Re: Should non-security 2.7 bugs be fixed?]

On Tue, Jul 21, 2015 at 7:10 PM, Marko Rauhamaa <marko@pacujo.net> wrote:
> This is getting deep. It is an embarrassing metamathematical fact that
> numbers cannot be defined. At least, mathematicians gave up trying a
> century ago.
>
>    In mathematics, the essence of counting a set and finding a result n,
>    is that it establishes a one to one correspondence (or bijection) of
>    the set with the set of numbers {1, 2, ..., n}.
>    <URL: https://en.wikipedia.org/wiki/Counting#Counting_in_mathematics>

AIUI, zero is defined as the cardinality of the empty set, one is
defined as the cardinality of the set containing the empty set, two is
defined as the cardinality of the set containing the empty set and the
set containing the set containing the empty set... which makes
mathematics the only language *more verbose* than the Shakespeare
Programming Language in its definition of fundamental constants.

ChrisA

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#94281 — Re: Devanagari int literals [was Re: Should non-security 2.7 bugs be fixed?]

Chris Angelico <rosuav@gmail.com>:

> On Tue, Jul 21, 2015 at 7:10 PM, Marko Rauhamaa <marko@pacujo.net> wrote:
>> This is getting deep. It is an embarrassing metamathematical fact
>> that numbers cannot be defined. At least, mathematicians gave up
>> trying a century ago.
>>
>>    In mathematics, the essence of counting a set and finding a result
>>    n, is that it establishes a one to one correspondence (or
>>    bijection) of the set with the set of numbers {1, 2, ..., n}.
>>    <URL: https://en.wikipedia.org/wiki/Counting#Counting_in_mathematics>
>
> AIUI, zero is defined as the cardinality of the empty set, one is
> defined as the cardinality of the set containing the empty set, two is
> defined as the cardinality of the set containing the empty set and the
> set containing the set containing the empty set... which makes
> mathematics the only language *more verbose* than the Shakespeare
> Programming Language in its definition of fundamental constants.

   There are two approaches to cardinality – one which compares sets
   directly using bijections and injections, and another which uses
   cardinal numbers.
   <URL: https://en.wikipedia.org/wiki/Cardinality>

The first approach is comparative, the second approach is quantitative.
You must be referring to the latter meaning (cardinality ~ cardinal
number). However:

   In mathematics, cardinal numbers, or cardinals for short, are a
   generalization of the natural numbers [...]
   <URL: https://en.wikipedia.org/wiki/Cardinal_number>

IOW, cardinal numbers assume natural numbers as a given. Thus, your
definition of natural numbers leads to a circular definition.

Frege et al tried to do the natural thing and defined natural numbers as
equivalence classes:

   0 = the set of sets with no elements
   1 = the set of sets with a single element
   2 = the set of sets with precisely two elements
   etc

Unfortunately, the natural thing leads to a contradiction and must be
abandoned.

Nowadays, mathematicians are content with working with one prototypical
chain of beads:

   0 = ∅
   1 = { 0 }
   2 = { 0, 1 }
   3 = { 0, 1, 2 }
   etc

IOW:

   0 = ∅
   σ(n) = n ∪ { n }

and forget about the true essence of numbers.


Marko

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#94282 — Re: Devanagari int literals [was Re: Should non-security 2.7 bugs be fixed?]

On 21/07/2015 10:10, Marko Rauhamaa wrote:
> Laura Creighton <lac@openend.se>:
>
>> In a message of Mon, 20 Jul 2015 20:30:48 -0700, Rustom Mody writes:
>>
>>> Can some unicode/Chinese literate person inform me whether that
>>> ideograph is equivalent to roman '9' or roman 'nine'?
>>
>> Ah, I don't understand you. What do you mean roman 'nine'? a phonetic
>> way of saying things? What bankers use to help prevent forgeries?
>> Something else?
>
> This is getting deep. It is an embarrassing metamathematical fact that
> numbers cannot be defined. At least, mathematicians gave up trying a
> century ago.
>
>     In mathematics, the essence of counting a set and finding a result n,
>     is that it establishes a one to one correspondence (or bijection) of
>     the set with the set of numbers {1, 2, ..., n}.
>     <URL: https://en.wikipedia.org/wiki/Counting#Counting_in_mathematics>
>
> Our ancestors defined the fingers (or digits) as "the set of numbers."
> Modern mathematicians have managed to enhance the definition
> quantitatively but not qualitatively.
>

Not all of them 
http://www.languagesandnumbers.com/how-to-count-in-paici/en/pri/

-- 
My fellow Pythonistas, ask not what our language can do for you, ask
what you can do for our language.

Mark Lawrence

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#94283 — Re: Devanagari int literals [was Re: Should non-security 2.7 bugs be fixed?]

On Tuesday 21 July 2015 19:10, Marko Rauhamaa wrote:


> This is getting deep.

When things get too deep, stop digging.


> It is an embarrassing metamathematical fact that
> numbers cannot be defined. At least, mathematicians gave up trying a
> century ago.

That's not the case. It's not so much that they stopped trying (implying 
failure), but that they succeeded, for some definition of success (see 
below).

The contemporary standard approach is from Zermelo-Fraenkel set theory: 
define 0 as the empty set, and the successor to n as the union of n and the 
set containing n:

0 = {} (the empty set) 
n + 1 = n ∪ {n}

https://en.wikipedia.org/wiki/Set-theoretic_definition_of_natural_numbers


> Our ancestors defined the fingers (or digits) as "the set of numbers."
> Modern mathematicians have managed to enhance the definition
> quantitatively but not qualitatively.

So what?

This is not a problem for the use of numbers in science, engineering or 
mathematics (including computer science, which may be considered a branch of 
all three). There may be still a few holdouts who hope that Gödel is wrong 
and Russell's dream of being able to define all of mathematics in terms of 
logic can be resurrected, but everyone else has moved on, and don't consider 
it to be "an embarrassment" any more than it is an embarrassment that all of 
philosophy collapses in a heap when faced with solipsism.

We have no reason to expect that the natural numbers are anything less than 
"absolutely fundamental and irreducible" (as the Wikipedia article above 
puts it). It's remarkable that we can reduce all of mathematics to 
essentially a single axiom: the concept of the set.


-- 
Steve

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#94284 — Re: Devanagari int literals [was Re: Should non-security 2.7 bugs be fixed?]

Steven D'Aprano <steve+comp.lang.python@pearwood.info>:

> That's not the case. It's not so much that they stopped trying (implying 
> failure), but that they succeeded, for some definition of success (see 
> below).
>
> The contemporary standard approach is from Zermelo-Fraenkel set theory: 
> define 0 as the empty set, and the successor to n as the union of n and the 
> set containing n:
>
> 0 = {} (the empty set) 
> n + 1 = n ∪ {n}

That definition barely captures the essence of what a number *is*. In
fact, there have been different formulations of natural numbers. For
example:

   0 = {}
   1 = {0}
   2 = {1}
   3 = {2}
   etc


Marko

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#95175 — Re: Devanagari int literals [was Re: Should non-security 2.7 bugs be fixed?]

Marko Rauhamaa <marko@pacujo.net>:

> Steven D'Aprano <steve+comp.lang.python@pearwood.info>:
>
>> The contemporary standard approach is from Zermelo-Fraenkel set
>> theory: define 0 as the empty set, and the successor to n as the
>> union of n and the set containing n:
>>
>> 0 = {} (the empty set) 
>> n + 1 = n ∪ {n}
>
> That definition barely captures the essence of what a number *is*. In
> fact, there have been different formulations of natural numbers.

Rehashing this old discussion. I ran into this wonderful website:

  <URL: http://at.metamath.org/mpeuni/mmset.html>

It is an absolute treasure for those of us who hate handwaving in math
textbooks. The database of computer-checked theorems proves everything
starting from the very bottom.

An interesting, recurring dividing line among the proofs is a layer of
"provable" axioms. For example, this proof

   http://at.metamath.org/mpeuni/2p2e4.html

(for "⊢ (2 + 2) = 4") references the axiom (<URL:
http://at.metamath.org/mpeuni/ax-1cn.html>):

   ⊢ 1 ∈ ℂ

The axiom is "justified by" a set-theoretic theorem:

   Description: 1 is a complex number. Axiom 2 of 22 for real and
   complex numbers, derived from ZF set theory. This
   construction-dependent theorem should not be referenced directly;
   instead, use ax-1cn 7963.
   <URL: http://at.metamath.org/mpeuni/ax1cn.html>

In other words, since there is no canonical way to define numbers in set
theory, Metamath insulates its proofs from a particular definition by
circumscribing numbers with construction-independent axioms.


Anyway, ob. Python reference:

   Using the design ideas implemented in Metamath, Raph Levien has
   implemented what might be the smallest proof checker in the world,
   mmverify.py, at only 500 lines of Python code.
   <URL: https://en.wikipedia.org/wiki/Metamath>


Marko

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#95193 — Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?]

On Sunday, August 9, 2015 at 2:57:20 AM UTC+5:30, Marko Rauhamaa wrote:
> Marko Rauhamaa :
> 
> > Steven D'Aprano :
> >
> >> The contemporary standard approach is from Zermelo-Fraenkel set
> >> theory: define 0 as the empty set, and the successor to n as the
> >> union of n and the set containing n:
> >>
> >> 0 = {} (the empty set) 
> >> n + 1 = n ∪ {n}
> >
> > That definition barely captures the essence of what a number *is*. In
> > fact, there have been different formulations of natural numbers.
> 
> Rehashing this old discussion. I ran into this wonderful website:
> 
>   <URL: http://at.metamath.org/mpeuni/mmset.html>

Attention you Hilbertian!
Gödelian here — http://blog.languager.org/2015/07/cs-history-2.html 
:-)
Thanks for that link. Need to study it carefully

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#94363 — Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?]

On Tuesday, July 21, 2015 at 4:09:56 PM UTC+5:30, Steven D'Aprano wrote:

> We have no reason to expect that the natural numbers are anything less than 
> "absolutely fundamental and irreducible" (as the Wikipedia article above 
> puts it). It's remarkable that we can reduce all of mathematics to 
> essentially a single axiom: the concept of the set.

These two statements above contradict each other.
With the double-negatives and other lint removed they read:

1. We have reason to expect that the natural numbers are absolutely fundamental and irreducible

2. We can reduce all of mathematics to essentially a single axiom: the concept of the set.

So are you on the number-side -- Poincare, Brouwer, Heyting...
Or the set-side -- Cantor, Russel, Hilbert... ??

> On Tuesday 21 July 2015 19:10, Marko Rauhamaa wrote:
> > Our ancestors defined the fingers (or digits) as "the set of numbers."
> > Modern mathematicians have managed to enhance the definition
> > quantitatively but not qualitatively.
> 
> So what?
> 
> This is not a problem for the use of numbers in science, engineering or 
> mathematics (including computer science, which may be considered a branch of 
> all three). There may be still a few holdouts who hope that Gödel is wrong 
> and Russell's dream of being able to define all of mathematics in terms of 
> logic can be resurrected, but everyone else has moved on, and don't consider 
> it to be "an embarrassment" any more than it is an embarrassment that all of 
> philosophy collapses in a heap when faced with solipsism.

That's a bizarre view.
As a subjective view "I dont feel embarrassed by..." its not arguable other than
to say embarrassment is like thick-skinnedness -- some have elephant-skins 
some have gossamer skins

As an objective view its just wrong: Eminent mathematicians have disagreed
so strongly with each other as to what putative math is kosher and what 
embarrassing that they've sent each other to mental institutions.

And -- most important of all -- these arguments are at the root of why CS 
'happened' : http://blog.languager.org/2015/03/cs-history-0.html

The one reason why this view -- "the embarrassments in math/logic foundations 
are no longer relevant as they were in the 1930s" -- is because people think
CS is mostly engineering, hardly math. So (the argument runs) just as general 
relativity is irrelevant to bridge-building, so also meta-mathematics is to pragmatic CS.

The answer to this view -- unfortunately widely-held -- is the same as above:
http://blog.languager.org/2015/03/cs-history-0.html
A knowledge of the history will disabuse of the holder of these misunderstandings
and misconceptions

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#94382 — OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?]

On Wed, 22 Jul 2015 11:34 pm, Rustom Mody wrote:

> On Tuesday, July 21, 2015 at 4:09:56 PM UTC+5:30, Steven D'Aprano wrote:
> 
>> We have no reason to expect that the natural numbers are anything less
>> than "absolutely fundamental and irreducible" (as the Wikipedia article
>> above puts it). It's remarkable that we can reduce all of mathematics to
>> essentially a single axiom: the concept of the set.
> 
> These two statements above contradict each other.
> With the double-negatives and other lint removed they read:

I meant what I said.

> 1. We have reason to expect that the natural numbers are absolutely
> fundamental and irreducible

That's wrong. If we had such a reason, we could state it: "the reason we
expect natural numbers are irreducible is ..." and fill in the blank. But I
don't believe that such a reason exists (or at least, as far as we know).

However, neither do we have any reason to think that they are *not*
irreducible. Hence, we have no reason to think that they are anything but
irreducible.


> 2. We can reduce all of mathematics to essentially a single axiom: the
> concept of the set.

Heh, yes, that is a bit funny. But I don't think it's really a
contradiction, because I don't think that numbers "really are" sets.

The set-theoretic definition of the natural numbers is quite nice, but is it
really simpler than the old fashioned idea of natural numbers as "counting
numbers"? Certainly it shows that we have a one-to-one correspondence from
the natural numbers to sets, building from the empty set alone, and in some
sense sets seem more primitive. But I think that proving that sets actually
are more primitive is another story.

I think that we can equally choose the natural numbers to be axiomatic, or
sets to be axiomatic and derive natural numbers from them. Neither is more
correct than the other.

By the way, my comment about "essentially a single axiom" should be read
informally. Formally, you need a whole bunch of axioms:

http://math.stackexchange.com/questions/68659/set-theoretic-construction-of-the-natural-numbers

I stated that the set-theoretic definition was generally accepted, but
that's quite far from saying it is logically proven. The definition comes
from Zermelo–Fraenkel set theory (ZF) plus the Axiom of Choice (ZFC), but
the Axiom of Choice is not uncontroversial. E.g. the  Banach-Tarski paradox
follows from AC.

https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox

Like any other Axiom, the Axiom of Choice is unprovable. You can either
accept it or reject it, and there is also ZF¬C. Jerry Bona jokes:

"The Axiom of Choice is obviously true, the well-ordering principle
obviously false, and who can tell about Zorn's lemma?"

the joke being that all three are mathematically equivalent.


> So are you on the number-side -- Poincare, Brouwer, Heyting...
> Or the set-side -- Cantor, Russel, Hilbert... ??

Yes. I think both points of view are useful, even if only useful in
understanding what the limits of that view are.


>> On Tuesday 21 July 2015 19:10, Marko Rauhamaa wrote:
>> > Our ancestors defined the fingers (or digits) as "the set of numbers."
>> > Modern mathematicians have managed to enhance the definition
>> > quantitatively but not qualitatively.
>> 
>> So what?
>> 
>> This is not a problem for the use of numbers in science, engineering or
>> mathematics (including computer science, which may be considered a branch
>> of all three). There may be still a few holdouts who hope that Gödel is
>> wrong and Russell's dream of being able to define all of mathematics in
>> terms of logic can be resurrected, but everyone else has moved on, and
>> don't consider it to be "an embarrassment" any more than it is an
>> embarrassment that all of philosophy collapses in a heap when faced with
>> solipsism.
> 
> That's a bizarre view.

Really? Which part(s) do you consider bizarre?

(1) That the lack of any fundamental definition of numbers in terms is not a
problem in practice?

(2) That comp sci can be considered a branch of science, engineering and
mathematics?

(3) That there may still be a few people who hope Gödel is wrong?

(4) That everyone else (well, at least everyone else in mathematics, for
some definition of "everyone") has moved on?

(5) That philosophy is unable to cope with the problem of solipsism?


I don't think any of those statements are *bizarre*, i.e. conspicuously or
grossly unconventional or unusual; eccentric; freakish; gonzo; outlandish;
outre; grotesque.

In hindsight, my claim of "everyone else" having moved on is too strong --
there are millions of mathematicians in the world, and I'm sure that you
can find one or two who don't fall into either of the two categories I
gave. That is, they neither wish to dispute Gödel nor do they accept the
irreducibility of numbers as something matter-of-fact and not embarrassing.
So let's just quietly insert an "almost" before "everyone" and move on,
shall we?


> As a subjective view "I dont feel embarrassed by..." its not arguable
> other than to say embarrassment is like thick-skinnedness -- some have
> elephant-skins some have gossamer skins

I don't think any of my comments relies on embarrassment being an objective
state.


> As an objective view its just wrong: Eminent mathematicians have disagreed
> so strongly with each other as to what putative math is kosher and what
> embarrassing that they've sent each other to mental institutions.

I think that the critical factor there is that it is all in the past tense.
Today, I believe, the vast majority of mathematicians fall into two camps:

(1) Those who just use numbers without worrying about defining them in some
deep or fundamental sense;

(2) Those who understand Gödel and have given up or rejected Russell's
program to define mathematics in terms of pure logic.


> And -- most important of all -- these arguments are at the root of why CS
> 'happened' : http://blog.languager.org/2015/03/cs-history-0.html

Again, this is the past.

> The one reason why this view -- "the embarrassments in math/logic
> foundations are no longer relevant as they were in the 1930s" -- is
> because people think CS is mostly engineering, hardly math. So (the
> argument runs) just as general relativity is irrelevant to
> bridge-building, so also meta-mathematics is to pragmatic CS.
> 
> The answer to this view -- unfortunately widely-held -- is the same as
> above: http://blog.languager.org/2015/03/cs-history-0.html
> A knowledge of the history will disabuse of the holder of these
> misunderstandings and misconceptions

I am very aware of the history of both comp sci and mathematics. It's not
that I think history is irrelevant. I think history is very important to
understand where we are, how we got here, and to where we are going.

It's that I think that Russell's program is a degenerate research program
and irrelevant paradigm abandoned by nearly everyone. Not only does Gödel
prove the impossibility of Russell's attempt to ground mathematics in pure
logic, but mathematicians have by and large rejected Russell's paradigm as
irrelevant, like quintessence or aether to physicists, or how many angels
can dance on the head of a pin to theologians. In simple terms, hardly
anyone cares how you define numbers, so long as the definition gives you
arithmetic.

Quoting Wikipedia:

"In the years following Gödel's theorems, as it became clear that there is
no hope of proving consistency of mathematics, and with development of
axiomatic set theories such as Zermelo–Fraenkel set theory and the lack of
any evidence against its consistency, most mathematicians lost interest in
the topic."

https://en.wikipedia.org/wiki/Finitism



-- 
Steven

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#94384 — Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?]

One way to look at this is to see that arithmetic is _behaviour_.
Like all behaviours, it is subject to reification:
see: https://en.wikipedia.org/wiki/Reification

and especially as it is done in the German language, reification has
this nasty habit of turning behaviours (i.e. things that are most like
a verb) into nouns, or things that require nouns.  Even the word
_behaviour_ is suspect, as it is a noun. 

This noun-making can be contagious .... if we thought of the world, not
as a thing, but happening-now (and see how hard it is to not have
a noun like 'process' there) would we come to the question of 'Who
made it?'  For there would be no 'it' there to point at.

It is not too surprising that the mathematicians have run into the
limits of reification.  There is only so much 'pretend this is a
thing' you can do under relentless questioning before the 'thing-ness'
just goes away ...

Laura

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#94388 — Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?]

Nice Thanks for that Laura!
I am reminded of

| The toughest job Indians ever had was explaining to the whiteman who their 
| noun-god is. Repeat. That's because God isn't a noun in Native America.
| God is a verb!
From http://hilgart.org/enformy/dma-god.htm

On Wednesday, July 22, 2015 at 10:48:38 PM UTC+5:30, Laura Creighton wrote:
> One way to look at this is to see that arithmetic is _behaviour_.
> Like all behaviours, it is subject to reification:
> see: https://en.wikipedia.org/wiki/Reification

This is just a pointer to various disciplines/definitions...
Which did you intend?
By and large (for me, a CSist) I regard reification as philosophicalese for
what programmers call first-classness.
As someone brought up on Lisp and FP, was trained to regard reification/firstclassness
as wonderful.  However after seeing the overwhelming stupidity of OOP-treated-as-a-philosophy,
Ive become suspect of this.
If http://steve-yegge.blogspot.in/2006/03/execution-in-kingdom-of-nouns.html
was just a joke it would be a laugh. I believe it is an accurate description
of the brain-pickling it does to its religious adherents.
And so now I am suspect of firstclassness in FP as well:
http://blog.languager.org/2012/08/functional-programming-philosophical.html
(last point)

> 
> and especially as it is done in the German language, reification has
> this nasty habit of turning behaviours (i.e. things that are most like
> a verb) into nouns, or things that require nouns.  Even the word
> _behaviour_ is suspect, as it is a noun. 
> 
> This noun-making can be contagious .... if we thought of the world, not
> as a thing, but happening-now (and see how hard it is to not have
> a noun like 'process' there) would we come to the question of 'Who
> made it?'  For there would be no 'it' there to point at.
> 
> It is not too surprising that the mathematicians have run into the
> limits of reification.  There is only so much 'pretend this is a
> thing' you can do under relentless questioning before the 'thing-ness'
> just goes away ...

Yes but one person's threshold where thing-ness can be far away from another's.
Newton used thingness of ∞ (infinitesimals) with impunity and invented calculus.
Gauss found this very improper and re-invented calculus without 'completed infinity'.
Yet mathematicians habitually find that, for example generating functions that
are obviously divergent (∴ semantically meaningless) are perfectly serviceable
to solve recurrences; solutions which can subsequently be verified without the
generating functions.
Which side should be embarrassed?

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#94392 — Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?]

In a message of Wed, 22 Jul 2015 10:49:13 -0700, Rustom Mody writes:
>Nice Thanks for that Laura!
>I am reminded of
>
>| The toughest job Indians ever had was explaining to the whiteman who their 
>| noun-god is. Repeat. That's because God isn't a noun in Native America.
>| God is a verb!
>>From http://hilgart.org/enformy/dma-god.htm
>
>On Wednesday, July 22, 2015 at 10:48:38 PM UTC+5:30, Laura Creighton wrote:
>> One way to look at this is to see that arithmetic is _behaviour_.
>> Like all behaviours, it is subject to reification:
>> see: https://en.wikipedia.org/wiki/Reification
>
>This is just a pointer to various disciplines/definitions...
>Which did you intend?

I meant -- depending on your background -- go find a meaning for
reification that makes sense to you.  And then extend this to some
other areas.

>By and large (for me, a CSist) I regard reification as philosophicalese for
>what programmers call first-classness.

Me too.  But there are more people out there who know something about
reification than there are that know about first classness.

>As someone brought up on Lisp and FP, was trained to regard reification/firstclassness
>as wonderful.  However after seeing the overwhelming stupidity of OOP-treated-as-a-philosophy,
>Ive become suspect of this.

>If http://steve-yegge.blogspot.in/2006/03/execution-in-kingdom-of-nouns.html
>was just a joke it would be a laugh. I believe it is an accurate description
>of the brain-pickling it does to its religious adherents.
>And so now I am suspect of firstclassness in FP as well:
>http://blog.languager.org/2012/08/functional-programming-philosophical.html
>(last point)
>
>> 
>> and especially as it is done in the German language, reification has
>> this nasty habit of turning behaviours (i.e. things that are most like
>> a verb) into nouns, or things that require nouns.  Even the word
>> _behaviour_ is suspect, as it is a noun. 
>> 
>> This noun-making can be contagious .... if we thought of the world, not
>> as a thing, but happening-now (and see how hard it is to not have
>> a noun like 'process' there) would we come to the question of 'Who
>> made it?'  For there would be no 'it' there to point at.
>> 
>> It is not too surprising that the mathematicians have run into the
>> limits of reification.  There is only so much 'pretend this is a
>> thing' you can do under relentless questioning before the 'thing-ness'
>> just goes away ...
>
>Yes but one person's threshold where thing-ness can be far away from another's.
>Newton used thingness of ∞ (infinitesimals) with impunity and invented calculus.
>Gauss found this very improper and re-invented calculus without 'completed infinity'.
>Yet mathematicians habitually find that, for example generating functions that
>are obviously divergent (∴ semantically meaningless) are perfectly serviceable
>to solve recurrences; solutions which can subsequently be verified without the
>generating functions.
>Which side should be embarrassed?

Embarassment is a function of the ego.  The ego is _another_ one of those nouns
where if you try to stalk it, it falls apart because it was produced by
behaviour, rather than the cause of behaviour.

Descartes:  I think, therefore I am.  (Because there must be an I that is
doing the thinking.)

Modern Day Western Neurologist:  Thinking is going on.  Therefore an I is
produced.

Laura

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#94399 — Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?]

On 22/07/2015 19:14, Laura Creighton wrote:

I don't suppose anybody could spare a bit of time for something that is 
slightly more important IMHO, like getting the core workflow going?

I'm fairly well convinced that the vast majority of people here aren't 
in the slightest bit interested in actually doing anything, but just in 
case you could try reading.

https://www.python.org/dev/peps/pep-0462/
https://www.python.org/dev/peps/pep-0474/

-- 
My fellow Pythonistas, ask not what our language can do for you, ask
what you can do for our language.

Mark Lawrence

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#94385 — Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?]

On Thu, 23 Jul 2015 02:58 am, Steven D'Aprano wrote:

>> 1. We have reason to expect that the natural numbers are absolutely
>> fundamental and irreducible
> 
> That's wrong. If we had such a reason, we could state it: "the reason we
> expect natural numbers are irreducible is ..." and fill in the blank. But
> I don't believe that such a reason exists (or at least, as far as we
> know).

Sorry, that's not as clear as I intended. By "a reason", I mean a direct
reason for that choice, rather than some reason for the opposite choice. I
hope that's clear? Perhaps an example will help.

"Are tomatoes red?"

We can have direct reasons for believing that tomatoes are red, e.g. "the
light reflecting off these tomatoes peaks at frequency X, which is within
the range of red light". 

Alternatively, we might not have any such reason, and be reduced to arguing
against the alternatives. Only if all the alternatives are false could we
then believe that tomatoes are red.

"If tomatoes were blue, they would appear green when viewed under yellow
light; since these tomatoes fail to appear green, they might be red."

I'm suggesting that we have no direct reason for believing that the natural
numbers are irreducible concepts, only indirect ones, namely that all the
attempts to reduce them are unsatisfactory in some fashion or another. But
neither do we have direct reasons for expecting them to be reducible.


-- 
Steven

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#94413 — Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?]

On Thu, 23 Jul 2015 03:21:24 +1000, Steven D'Aprano <steve@pearwood.info>
declaimed the following:

>
>"Are tomatoes red?"
>
	In answer I offer a novel: /Fried Green Tomatoes at the Whistle Stop
Cafe/ (and lots of recipes for such on Google)
-- 
	Wulfraed                 Dennis Lee Bieber         AF6VN
    wlfraed@ix.netcom.com    HTTP://wlfraed.home.netcom.com/

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#94414 — Re: OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?]

On Thu, Jul 23, 2015 at 11:44 AM, Dennis Lee Bieber
<wlfraed@ix.netcom.com> wrote:
> On Thu, 23 Jul 2015 03:21:24 +1000, Steven D'Aprano <steve@pearwood.info>
> declaimed the following:
>
>>
>>"Are tomatoes red?"
>>
>         In answer I offer a novel: /Fried Green Tomatoes at the Whistle Stop
> Cafe/ (and lots of recipes for such on Google)

I think we can take it as red.

*dives for cover*

ChrisA

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