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Re: Decimals and other numbers

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Date Fri, 09 Jan 2015 02:49:27 -0500
From Dave Angel <davea@davea.name>
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Subject Re: Decimals and other numbers
References <CABicbJK-5izGtet8BsS1Yqx+6AHMX7gLU4zYjjt5jULJXNVipA@mail.gmail.com> <54AF405C.6020609@davea.name> <mailman.17501.1420772593.18130.python-list@python.org> <87a91s1kh4.fsf@elektro.pacujo.net> <CAPTjJmrhZYw9vBhN6TUMuqFCL48SMNgSAYhAi5u27R4HWaDmUg@mail.gmail.com>
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On 01/09/2015 02:37 AM, Chris Angelico wrote:
> On Fri, Jan 9, 2015 at 6:28 PM, Marko Rauhamaa <marko@pacujo.net> wrote:
>> Devin Jeanpierre <jeanpierreda@gmail.com>:
>>
>>> If 0**0 is defined, it must be 1.
>>
>> You can "justify" any value a within [0, 1]. For example, choose
>>
>>     y(a, x) = log(a, x)
>>
>> Then,
>>
>>      lim    y(a, x) = 0
>>     x -> 0+
>>
>> and:
>>
>>     lim[x -> 0+] x**y(a, x) = a
>>
>> For example,
>>
>>     >>> a = 0.5
>>     >>> x = 1e-100
>>     >>> y = math.log(a, x)
>>     >>> y
>>     0.0030102999566398118
>>     >>> x**y
>>     0.5
>
> I'm not a mathematical expert, so I don't quite 'get' this. How does
> this justify 0**0 being equal to 0.5?
>
> I know how to justify 0 and 1, and NaN (on the basis that both 0 and 1
> can be justified). I don't follow how other values can be used.

Roughly speaking, the idea is to have a relationship between x and y, 
such that even though they each get arbitrarily close to zero, the 
formula x**y is a constant 5.

So he plugged in 1e-100.  But if you plugged in 1e-500000000  and could 
handle the precision, the result x**y  would still be 0.5




-- 
DaveA

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Thread

Re: Decimals and other numbers Devin Jeanpierre <jeanpierreda@gmail.com> - 2015-01-08 19:02 -0800
  Re: Decimals and other numbers Marko Rauhamaa <marko@pacujo.net> - 2015-01-09 09:28 +0200
    Re: Decimals and other numbers Chris Angelico <rosuav@gmail.com> - 2015-01-09 18:37 +1100
      Re: Decimals and other numbers Marko Rauhamaa <marko@pacujo.net> - 2015-01-09 11:31 +0200
    Re: Decimals and other numbers Dave Angel <davea@davea.name> - 2015-01-09 02:49 -0500
    Re: Decimals and other numbers Devin Jeanpierre <jeanpierreda@gmail.com> - 2015-01-09 00:51 -0800
      Re: Decimals and other numbers Jussi Piitulainen <jpiitula@ling.helsinki.fi> - 2015-01-09 11:07 +0200
        [OT] x**y == y**x Peter Pearson <pkpearson@nowhere.invalid> - 2015-01-09 17:46 +0000
          Re: [OT] x**y == y**x Marko Rauhamaa <marko@pacujo.net> - 2015-01-09 23:41 +0200
            Re: [OT] x**y == y**x Peter Pearson <pkpearson@nowhere.invalid> - 2015-01-10 16:57 +0000
  Re: Decimals and other numbers Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-01-09 19:49 +1100
    Re: Decimals and other numbers Devin Jeanpierre <jeanpierreda@gmail.com> - 2015-01-09 00:58 -0800
      Re: Decimals and other numbers Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-01-09 21:20 +1100
        Re: Decimals and other numbers Chris Angelico <rosuav@gmail.com> - 2015-01-09 21:39 +1100
          Re: Decimals and other numbers Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-01-09 23:24 +1100
            Re: Decimals and other numbers Chris Angelico <rosuav@gmail.com> - 2015-01-09 23:34 +1100
        Re: Decimals and other numbers Devin Jeanpierre <jeanpierreda@gmail.com> - 2015-01-09 17:25 -0800
        Re: Decimals and other numbers Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2015-01-10 16:08 +1300
    Re: Decimals and other numbers Devin Jeanpierre <jeanpierreda@gmail.com> - 2015-01-09 01:11 -0800
    Re: Decimals and other numbers Marko Rauhamaa <marko@pacujo.net> - 2015-01-09 11:34 +0200
      Re: Decimals and other numbers Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-01-09 22:03 +1100
    Re: Decimals and other numbers Marko Rauhamaa <marko@pacujo.net> - 2015-01-09 11:44 +0200
    Re: Decimals and other numbers Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2015-01-10 16:05 +1300
      Re: Decimals and other numbers Devin Jeanpierre <jeanpierreda@gmail.com> - 2015-01-09 19:57 -0800

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