Re: Encapsulation, inheritance and polymorphism

Date	2012-07-21 14:32 -0700
From	Erik Max Francis <max@alcyone.com>
Organization	Alcyone Systems
Newsgroups	comp.lang.python
Subject	Re: Encapsulation, inheritance and polymorphism
References	(16 earlier) <CAPTjJmrCht7Zcja4Ov+LJ2botgzWR8YtbgvM5hC2AkQSY0Xk4A@mail.gmail.com> <mailman.2312.1342723772.4697.python-list@python.org> <500912bb$0$29978$c3e8da3$5496439d@news.astraweb.com> <GsKdnWOQPKOOvZTNnZ2dnUVZ5s2dnZ2d@giganews.com> <jubbtg$mf3$1@dont-email.me>
Message-ID	<Oc-dnUqKG91pgpbNnZ2dnUVZ5vGdnZ2d@giganews.com> (permalink)

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On 07/20/2012 03:28 AM, BartC wrote:
> "Erik Max Francis" <max@alcyone.com> wrote in message
> news:GsKdnWOQPKOOvZTNnZ2dnUVZ5s2dnZ2d@giganews.com...
>> On 07/20/2012 01:11 AM, Steven D'Aprano wrote:
>>> On Thu, 19 Jul 2012 13:50:36 -0500, Tim Chase wrote:
>
>>> I'm reminded of Graham's Number, which is so large that there aren't
>>> enough molecules in the universe to write it out as a power tower
>>> a^b^c^d^..., or even in a tower of hyperpowers a^^b^^c^^d^^... It was
>>> the
>>> provable upper bound to a question to which experts in the field thought
>>> the most likely answer was ... six.
>>>
>>> (The bounds have since been reduced: the lower bound is now 13, and the
>>> upper bound is *much* smaller than Graham's Number but still
>>> inconceivably ginormous.)
>>
>> You don't even need to go that high. Even a run-of-the-mill googol
>> (10^100) is far larger than the total number of elementary particles in
>> the observable Universe.
>
> But you can write it down, even as a straightforward number, without any
> problem. Perhaps a googolplex (10^10^100 iirc) would be difficult to
> write it down in full, but I have just represented it as an exponent
> with little difficulty.
>
> These bigger numbers can't be written down, because there will never be
> enough material, even using multiple systems of exponents.

But that's true for precisely the same reason as what I said.  If you're 
going to write a number down in standard format (whatever the base), 
then the number of digits needed scales as the logarithm of the number 
(again, whatever the base).  log_10 10^100 is trivially 100, so a rough 
order of magnitude in that form is easy to write down.  But the log_10 
10^10^100 is 10^100 = a googol, which is already more than the number of 
elementary particles in the observable Universe.

> (A few years ago the biggest number I'd heard of was Skewes' Number
> (something like 10^10^10^34), but even that is trivial to write using
> conventional exponents as I've just shown. Graham's Number is in a
> different
> class altogether.)

Anything's trivial to "write down."  Just say "the number such that ..." 
and you've written it down.  Even "numbers" that aren't really numbers, 
such as transfinite cardinals!

-- 
Erik Max Francis && max@alcyone.com && http://www.alcyone.com/max/
  San Jose, CA, USA && 37 18 N 121 57 W && AIM/Y!M/Jabber erikmaxfrancis
   She's your moon, she's your sun / She could even be the one
    -- Nik Kershaw

Thread

Encapsulation, inheritance and polymorphism Lipska the Kat <lipska@lipskathekat.com> - 2012-07-17 09:45 +0100
  Re: Encapsulation, inheritance and polymorphism Devin Jeanpierre <jeanpierreda@gmail.com> - 2012-07-17 06:03 -0400
    Re: Encapsulation, inheritance and polymorphism Lipska the Kat <lipska@lipskathekat.com> - 2012-07-17 12:24 +0100
      Re: Encapsulation, inheritance and polymorphism Larry Hudson <orgnut@yahoo.com> - 2012-07-18 00:10 -0700
  Re: Encapsulation, inheritance and polymorphism Ulrich Eckhardt <ulrich.eckhardt@dominolaser.com> - 2012-07-17 11:30 +0200
    Re: Encapsulation, inheritance and polymorphism Lipska the Kat <lipska@lipskathekat.com> - 2012-07-17 12:01 +0100
      Re: Encapsulation, inheritance and polymorphism Dave Angel <d@davea.name> - 2012-07-17 07:23 -0400
      Re: Encapsulation, inheritance and polymorphism Andrew Berg <bahamutzero8825@gmail.com> - 2012-07-17 06:37 -0500
        Re: Encapsulation, inheritance and polymorphism Lipska the Kat <lipska@lipskathekat.com> - 2012-07-17 12:44 +0100
          Re: Encapsulation, inheritance and polymorphism Andrew Berg <bahamutzero8825@gmail.com> - 2012-07-17 06:53 -0500
          Re: Encapsulation, inheritance and polymorphism Mark Lawrence <breamoreboy@yahoo.co.uk> - 2012-07-17 14:35 +0100
        Re: Encapsulation, inheritance and polymorphism Lipska the Kat <lipska@lipskathekat.com> - 2012-07-17 15:01 +0100
          Re: Encapsulation, inheritance and polymorphism Andrew Berg <bahamutzero8825@gmail.com> - 2012-07-17 09:16 -0500
            Re: Encapsulation, inheritance and polymorphism Lipska the Kat <lipska@lipskathekat.com> - 2012-07-17 15:26 +0100
          Re: Encapsulation, inheritance and polymorphism Terry Reedy <tjreedy@udel.edu> - 2012-07-17 13:30 -0400
          Re: Encapsulation, inheritance and polymorphism Andrew Berg <bahamutzero8825@gmail.com> - 2012-07-17 12:57 -0500
      Re: Encapsulation, inheritance and polymorphism Ulrich Eckhardt <ulrich.eckhardt@dominolaser.com> - 2012-07-17 14:18 +0200
      Re: Encapsulation, inheritance and polymorphism Mark Lawrence <breamoreboy@yahoo.co.uk> - 2012-07-17 14:29 +0100
      Re: Encapsulation, inheritance and polymorphism Roy Smith <roy@panix.com> - 2012-07-17 09:52 -0400
        Re: Encapsulation, inheritance and polymorphism Lipska the Kat <lipska@lipskathekat.com> - 2012-07-17 15:23 +0100
          Re: Encapsulation, inheritance and polymorphism Mark Lawrence <breamoreboy@yahoo.co.uk> - 2012-07-17 17:26 +0100
            Re: Encapsulation, inheritance and polymorphism Lipska the Kat <lipska@lipskathekat.com> - 2012-07-17 17:46 +0100
          Re: Encapsulation, inheritance and polymorphism Terry Reedy <tjreedy@udel.edu> - 2012-07-17 13:07 -0400
            Re: Encapsulation, inheritance and polymorphism Lipska the Kat <lipska@lipskathekat.com> - 2012-07-17 20:29 +0100
              Re: Encapsulation, inheritance and polymorphism Mark Lawrence <breamoreboy@yahoo.co.uk> - 2012-07-17 20:39 +0100
                Re: Encapsulation, inheritance and polymorphism Lipska the Kat <lipska@lipskathekat.com> - 2012-07-17 20:52 +0100
                Re: Encapsulation, inheritance and polymorphism John Ladasky <john_ladasky@sbcglobal.net> - 2012-08-18 23:05 -0700
                Re: Encapsulation, inheritance and polymorphism John Ladasky <john_ladasky@sbcglobal.net> - 2012-08-18 23:05 -0700
              Re: Encapsulation, inheritance and polymorphism Dennis Lee Bieber <wlfraed@ix.netcom.com> - 2012-07-17 18:57 -0400
          Re: Encapsulation, inheritance and polymorphism Ethan Furman <ethan@stoneleaf.us> - 2012-07-17 10:29 -0700
          Re: Encapsulation, inheritance and polymorphism Chris Angelico <rosuav@gmail.com> - 2012-07-18 04:01 +1000
          Re: Encapsulation, inheritance and polymorphism Tim Chase <python.list@tim.thechases.com> - 2012-07-17 12:51 -0500
          Re: Encapsulation, inheritance and polymorphism Mark Lawrence <breamoreboy@yahoo.co.uk> - 2012-07-17 19:18 +0100
            Re: Encapsulation, inheritance and polymorphism Lipska the Kat <lipska@lipskathekat.com> - 2012-07-17 19:36 +0100
              Re: Encapsulation, inheritance and polymorphism Andrew Cooper <amc96@cam.ac.uk> - 2012-07-18 01:46 +0100
                Re: Encapsulation, inheritance and polymorphism rusi <rustompmody@gmail.com> - 2012-07-17 20:54 -0700
                Re: Encapsulation, inheritance and polymorphism Lipska the Kat <lipska@lipskathekat.com> - 2012-07-18 10:06 +0100
                Re: Encapsulation, inheritance and polymorphism Ulrich Eckhardt <ulrich.eckhardt@dominolaser.com> - 2012-07-18 14:01 +0200
                Re: Encapsulation, inheritance and polymorphism "BartC" <bc@freeuk.com> - 2012-07-19 01:41 +0100
                Re: Encapsulation, inheritance and polymorphism Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2012-07-18 13:05 +0000
                Re: Encapsulation, inheritance and polymorphism Lipska the Kat <lipska@lipskathekat.com> - 2012-07-18 15:40 +0100
                Re: Encapsulation, inheritance and polymorphism Chris Angelico <rosuav@gmail.com> - 2012-07-19 01:04 +1000
                Re: Encapsulation, inheritance and polymorphism Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2012-07-19 01:22 +0000
                Re: Encapsulation, inheritance and polymorphism Chris Angelico <rosuav@gmail.com> - 2012-07-19 15:09 +1000
                Re: Encapsulation, inheritance and polymorphism Ethan Furman <ethan@stoneleaf.us> - 2012-07-18 08:32 -0700
                Re: Encapsulation, inheritance and polymorphism Lipska the Kat <lipska@lipskathekat.com> - 2012-07-18 16:49 +0100
                Re: Encapsulation, inheritance and polymorphism Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2012-07-19 01:34 +0000
                Re: Encapsulation, inheritance and polymorphism rusi <rustompmody@gmail.com> - 2012-07-18 23:09 -0700
                Re: Encapsulation, inheritance and polymorphism Lipska the Kat <lipska@lipskathekat.com> - 2012-07-19 09:56 +0100
                Re: Encapsulation, inheritance and polymorphism rusi <rustompmody@gmail.com> - 2012-07-19 08:58 -0700
                Re: Encapsulation, inheritance and polymorphism Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2012-07-19 12:59 +0000
                Re: Encapsulation, inheritance and polymorphism Roy Smith <roy@panix.com> - 2012-07-19 09:06 -0400
                Re: Encapsulation, inheritance and polymorphism Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2012-07-20 07:24 +0000
                Re: Encapsulation, inheritance and polymorphism rusi <rustompmody@gmail.com> - 2012-07-20 01:21 -0700
                Re: Encapsulation, inheritance and polymorphism Paul Rudin <paul.nospam@rudin.co.uk> - 2012-07-19 18:22 +0100
                Re: Encapsulation, inheritance and polymorphism Tim Chase <python.list@tim.thechases.com> - 2012-07-19 13:20 -0500
                Re: Encapsulation, inheritance and polymorphism Chris Angelico <rosuav@gmail.com> - 2012-07-20 04:28 +1000
                Re: Encapsulation, inheritance and polymorphism Tim Chase <python.list@tim.thechases.com> - 2012-07-19 13:50 -0500
                Re: Encapsulation, inheritance and polymorphism Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2012-07-20 08:11 +0000
                Re: Encapsulation, inheritance and polymorphism Erik Max Francis <max@alcyone.com> - 2012-07-20 02:08 -0700
                Re: Encapsulation, inheritance and polymorphism "BartC" <bc@freeuk.com> - 2012-07-20 11:28 +0100
                Re: Encapsulation, inheritance and polymorphism Erik Max Francis <max@alcyone.com> - 2012-07-21 14:32 -0700
                Re: Encapsulation, inheritance and polymorphism Albert van der Horst <albert@spenarnc.xs4all.nl> - 2012-07-23 16:36 +0000
                Re: Encapsulation, inheritance and polymorphism Dennis Lee Bieber <wlfraed@ix.netcom.com> - 2012-07-19 16:47 -0400
                Re: Encapsulation, inheritance and polymorphism John Gordon <gordon@panix.com> - 2012-07-19 21:01 +0000
                Re: Encapsulation, inheritance and polymorphism Chris Angelico <rosuav@gmail.com> - 2012-07-20 08:20 +1000
                Re: Encapsulation, inheritance and polymorphism John Gordon <gordon@panix.com> - 2012-07-19 22:23 +0000
                Re: Encapsulation, inheritance and polymorphism Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2012-07-20 08:27 +0000
                Re: Encapsulation, inheritance and polymorphism Virgil Stokes <vs@it.uu.se> - 2012-07-20 11:05 +0200
                Re: Encapsulation, inheritance and polymorphism Hans Mulder <hansmu@xs4all.nl> - 2012-07-20 19:45 +0200
                Re: Encapsulation, inheritance and polymorphism Erik Max Francis <max@alcyone.com> - 2012-07-21 14:28 -0700
                Re: Encapsulation, inheritance and polymorphism Dennis Lee Bieber <wlfraed@ix.netcom.com> - 2012-07-20 13:57 -0400
                Re: Encapsulation, inheritance and polymorphism Ian Kelly <ian.g.kelly@gmail.com> - 2012-07-19 15:13 -0600
                Re: Encapsulation, inheritance and polymorphism Devin Jeanpierre <jeanpierreda@gmail.com> - 2012-07-19 17:30 -0400
                Re: Encapsulation, inheritance and polymorphism Mark Lawrence <breamoreboy@yahoo.co.uk> - 2012-07-20 10:00 +0100
                Re: Encapsulation, inheritance and polymorphism Terry Reedy <tjreedy@udel.edu> - 2012-07-19 02:11 -0400
                Re: Encapsulation, inheritance and polymorphism Albert van der Horst <albert@spenarnc.xs4all.nl> - 2012-07-23 16:18 +0000
                Re: Encapsulation, inheritance and polymorphism Chris Angelico <rosuav@gmail.com> - 2012-07-24 02:15 +1000
                Re: Encapsulation, inheritance and polymorphism Robert Miles <robertmiles@teranews.com> - 2012-08-19 00:21 -0500
                Re: Encapsulation, inheritance and polymorphism Mark Lawrence <breamoreboy@yahoo.co.uk> - 2012-08-19 09:55 +0100
                Re: Encapsulation, inheritance and polymorphism lipska the kat <lipskathekat@yahoo.co.uk> - 2012-08-19 12:50 +0100
                Re: Encapsulation, inheritance and polymorphism Mark Lawrence <breamoreboy@yahoo.co.uk> - 2012-08-19 13:06 +0100
          Re: Encapsulation, inheritance and polymorphism Ethan Furman <ethan@stoneleaf.us> - 2012-07-17 11:43 -0700
          Re: Encapsulation, inheritance and polymorphism Devin Jeanpierre <jeanpierreda@gmail.com> - 2012-07-17 15:05 -0400
          Re: Encapsulation, inheritance and polymorphism Mark Lawrence <breamoreboy@yahoo.co.uk> - 2012-07-17 20:33 +0100
          Re: Encapsulation, inheritance and polymorphism Ian <hobson42@gmail.com> - 2012-07-17 19:59 +0100
        Re: Encapsulation, inheritance and polymorphism Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2012-07-18 12:58 +0000
          Re: Encapsulation, inheritance and polymorphism Roy Smith <roy@panix.com> - 2012-07-18 09:07 -0400
            Re: Encapsulation, inheritance and polymorphism Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2012-07-18 14:31 +0000
          Re: Encapsulation, inheritance and polymorphism Dave Angel <d@davea.name> - 2012-07-18 12:33 -0400
            Re: Encapsulation, inheritance and polymorphism Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2012-07-19 01:23 +0000
      Re: Encapsulation, inheritance and polymorphism Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2012-07-18 12:43 +0000
      Re: Encapsulation, inheritance and polymorphism Grant Edwards <invalid@invalid.invalid> - 2012-07-18 14:34 +0000
        Re: Encapsulation, inheritance and polymorphism Lipska the Kat <lipska@lipskathekat.com> - 2012-07-18 15:48 +0100
          Re: Encapsulation, inheritance and polymorphism Chris Angelico <rosuav@gmail.com> - 2012-07-19 01:09 +1000
            Re: Encapsulation, inheritance and polymorphism Lipska the Kat <lipska@lipskathekat.com> - 2012-07-18 16:36 +0100
          Re: Encapsulation, inheritance and polymorphism Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2012-07-19 01:14 +0000
            Re: Encapsulation, inheritance and polymorphism MRAB <python@mrabarnett.plus.com> - 2012-07-19 02:28 +0100
              Re: Encapsulation, inheritance and polymorphism "OKB (not okblacke)" <brenNOSPAMbarn@NObrenSPAMbarn.net> - 2012-07-19 16:52 +0000
        Re: Encapsulation, inheritance and polymorphism Andrew Berg <bahamutzero8825@gmail.com> - 2012-07-18 10:00 -0500
  Re: Encapsulation, inheritance and polymorphism Lipska the Kat <lipska@lipskathekat.com> - 2012-07-17 13:01 +0100
    Re: Encapsulation, inheritance and polymorphism Terry Reedy <tjreedy@udel.edu> - 2012-07-17 13:24 -0400
      Re: Encapsulation, inheritance and polymorphism Lipska the Kat <lipska@lipskathekat.com> - 2012-07-17 19:21 +0100
    Re: Encapsulation, inheritance and polymorphism MRAB <python@mrabarnett.plus.com> - 2012-07-17 18:43 +0100
    Re: Encapsulation, inheritance and polymorphism Tim Chase <python.list@tim.thechases.com> - 2012-07-17 12:56 -0500
    Re: Encapsulation, inheritance and polymorphism Arnaud Delobelle <arnodel@gmail.com> - 2012-07-18 11:35 +0100

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