Please rid me of this goto

[H. S. Teoh via Digitalmars-d]

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

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.

Mathematicians arbitrarily chose its value to be 1 based on arguments
like the one Timon gave, but it's an arbitrary choice, not something
that the mathematics itself suggest.


T

-- 
Try to keep an open mind, but not so open your brain falls out. -- theboz