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Re: Decimals and other numbers

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On Fri, Jan 9, 2015 at 9:20 PM, Steven D'Aprano
<steve+comp.lang.python@pearwood.info> wrote:
> On the basis that m**n means m multiplied by itself n times:
>
> 5**4 = 5*5*5*5 = 625
>
> that gives us:
>
> 0**0 = zero multiplied by itself zero times.
>
> You can multiply 0 by any number you like, and the answer will always be 0,
> not 1. Even if that other number is 0, the answer is still 0.

5 * 0 * 0 * 0 * 0 = 0

You can multiply 5 by 0 any number of times you like, and the answer
will always be 0... unless you never multiply it by 0 at all, in which
case it'll be 5. Multiplying 0 by any number, including 0, is 0... but
*not* multiplying 0 by 0 doesn't have to give 0. 0**0 is the result of
not multiplying any zeroes together, so it doesn't follow the rules of
multiplying zeroes together.

Look at it another way. 6**x modulo 10 will always be 6, right? 6, 36,
216... the rules for multiplying mean that the last digit will be
consistent. (That's how we can know what the last digits of Graham's
Number are, despite having no way to even comprehend its scale.) So
what's 6**0? Is that going to end with 6, too, to be consistent? No,
because we're not multiplying any sixes in, so the answer's simply 1.

ChrisA

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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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