Decimals and other numbers
Dave Angel
davea at davea.name
Fri Jan 9 08:49:27 CET 2015
On 01/09/2015 02:37 AM, Chris Angelico wrote:
> 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.
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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