Decimals and other numbers

[Chris Angelico]

On Fri, Jan 9, 2015 at 6:28 PM, Marko Rauhamaa <marko at pacujo.net> wrote:
> Devin Jeanpierre <jeanpierreda at 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.

ChrisA