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Re: Decimals and other numbers

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On Fri, Jan 9, 2015 at 7:05 PM, Gregory Ewing
<greg.ewing@canterbury.ac.nz> wrote:
> It's far from clear what *anything* multiplied by
> itself zero times should be.
>
> A better way of thinking about what x**n for integer
> n means is this: Start with 1, and multiply it by
> x n times. The result of this is clearly 1 when n
> is 0, regardless of the value of x.
>
>> 5**4 = 5*5*5*5 = 625
>
> No:
>
> 5**4 = 1*5*5*5*5
> 5**3 = 1*5*5*5
> 5**2 = 1*5*5
> 5**1 = 1*5
> 5**0 = 1

I never liked that, it seemed too arbitrary. How about this explanation:

Assume that we know how to multiply a nonempty list numbers. so
product([a]) == a, product([a, b]) = a * b, and so on.

def product(nums):
    if len(nums) == 0:
        return ???
    return reduce(operator.mul, nums)

It should be the case that given a list of factors A and B,
product(A + B) == product(A) * product(B)   (associativity).
We should let this rule apply even if A or B is the empty list,
otherwise our rules are kind of stupid.

Therefore, product([] + X) == product([]) * product(X)
But since [] + X == X, product([] + X) == product(X)

There's only one number like that: product([]) == 1

(Of course if you choose not to have the full associativity rule for
empty products, then anything is possible.)

-- Devin

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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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