Decimals and other numbers

Marko Rauhamaa marko at pacujo.net
Fri Jan 9 08:28:23 CET 2015


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


Marko



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