Please rid me of this goto

[Timon Gehr via Digitalmars-d]

On 24.06.2016 01:18, H. S. Teoh via Digitalmars-d wrote:
> On Thu, Jun 23, 2016 at 11:14:08PM +0000, deadalnix via Digitalmars-d wrote:
>> On Thursday, 23 June 2016 at 22:53:59 UTC, H. S. Teoh wrote:
>>> This argument only works for discrete sets.  If n and m are reals,
>>> you'd need a different argument.
>>>
>>
>> For reals, you can use limits/continuation as argument.
>
> The problem with that is that you get two different answers:
>
> 	lim  x^y = 0
> 	x->0
>
> but:
>
> 	lim  x^y = 1
> 	y->0
> ...

That makes no sense. You want lim[x->0] x^0 and lim[y->0] 0^y.

> So it's not clear what ought to happen when both x and y approach 0.
>
> The problem is that the 2-variable function f(x,y)=x^y has a
> discontinuity at (0,0). So approaching it from some directions give 1,
> approaching it from other directions give 0, and it's not clear why one
> should choose the value given by one direction above another.
> ...

It is /perfectly/ clear. What makes you so invested in the continuity of 
the function 0^y? It's just not important.

> Mathematicians arbitrarily chose its value to be 1 based on arguments
> like the one Timon gave, but it's an arbitrary choice,

It is absolutely /not/ arbitrary.

> not something that the mathematics itself suggest.
> ...

What kind of standard is that? 'The mathematics itself' does not suggest 
that we do not define 2+2=5 while keeping all other function values 
intact either, and it is still obvious to everyone that it would be a 
bad idea to give such succinct notation to such an unimportant function.