Measuring Fractal Dimension ?

[pdpi]

On Jun 23, 6:49 pm, Lie Ryan <lie.1... at gmail.com> wrote:
> Mark Dickinson wrote:
> > On Jun 23, 3:52 am, Steven D'Aprano
> > <ste... at REMOVE.THIS.cybersource.com.au> wrote:
> >> On Mon, 22 Jun 2009 13:43:19 -0500, David C. Ullrich wrote:
> >>> In my universe the standard definition of "log" is different froim what
> >>> log means in a calculus class
> >> Now I'm curious what the difference is.
>
> > It's just the usual argument about whether 'log' means
> > log base 10 or log base e (natural log).  At least in the
> > US, most[*] calculus texts (and also most calculators),
> > for reasons best known to themselves, use 'ln' to mean
> > natural log and 'log' to mean log base 10.  But most
> > mathematicians use 'log' to mean natural log:  pick up a
> > random pure mathematics research paper that has the word
> > 'log' in it, and unless it's otherwise qualified, it's
> > safe to assume that it means log base e.  (Except in the
> > context of algorithmic complexity, where it might well
> > mean log base 2 instead...)
>
> I usually use log without explicit base only when the base isn't
> relevant in the context (i.e. when whatever sane base you put in it
> wouldn't really affect the operations). In algorithmic complexity, a
> logarithm's base doesn't affect the growth shape and, like constant
> multiplier, is considered irrelevant to the complexity.
>
> > Python also suffers a bit from this confusion:  the
> > Decimal class defines methods 'ln' and 'log10', while
> > the math module and cmath modules define 'log' and
> > 'log10'.  
>
> In fact, in the Decimal class there is no log to an arbitrary base.
>
> > (But the Decimal module has other problems,
> > like claiming that 0**0 is undefined while
> > infinity**0 is 1.)
>
> Well, in math inf**0 is undefined. Since python is programming language,
> and in language standards it is well accepted that undefined behavior
> means implementations can do anything they like including returning 0,
> 1, 42, or even spitting errors, that doesn't make python non-conforming
> implementation.
>
> A more serious argument: in IEEE 745 float, inf**0 is 1. Mathematic
> operation in python is mostly a wrapper for the underlying C library's
> sense of math.
>
>
>
> > [*] A notable exception is Michael Spivak's 'Calculus', which also
> > happens to be the book I learnt calculus from many years ago.

Well, AFAIK Python defines CPython as the standard. So whatever
CPython does is the defined behaviour.

Regarding inf ** 0, why does IEEE745 define it as 1, when there is a
perfectly fine NaN value?