Please rid me of this goto

[H. S. Teoh via Digitalmars-d]

On Fri, Jun 24, 2016 at 01:33:46AM +0200, Timon Gehr via Digitalmars-d wrote:
> On 24.06.2016 00:53, H. S. Teoh via Digitalmars-d wrote:
> > > >Because 0^^0 = 1, and 1 is representable.
> > > >
> > > >E.g. n^^m counts the number of functions from an m-set to an n-set,
> > > >and there is exactly one function from {} to {}.
> > This argument only works for discrete sets.
> 
> No, it works for any cardinals n and m.

It doesn't.  What is the meaning of m-set and n-set when m and n are
real numbers?  How many elements are in a pi-set?  How many functions
are there from a pi-set to an e-set?  Your "number of functions"
argument only works if m and n are discrete numbers.


> > If n and m are reals, you'd need a different argument.
> > 
> 
> I don't want to argue this at all. x^^0 is an empty product no matter
> what set I choose x and 0 from.

And 0^^x is a non-empty product when x != 0.  So why should we choose
the limit of x^^0 as opposed to the limit of 0^^x?


> 0^^0 = 1 is the only reasonable convention, and this is absolutely
> painfully obvious from where I stand. What context are you using 'pow'
> in that would suggest otherwise?

When computing the limit of x^y as x->0?


> Also, Andrei's implementation explicitly works on integers anyway.

Even for integers, the limit of x^y as x->0 is 0.

My point is that the choice is an arbitrary one. It doesn't arise
directly from the mathematics itself.  I understand that 0^0 is chosen
to equal 1 in order for certain theorems to be more "aesthetically
beautiful", just like 0! is chosen to equal 1 because it makes the
definition of factorial "nicer". But it's still an arbitrary choice.


T

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