On Thursday, 23 June 2016 at 23:18:03 UTC, H. S. Teoh 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
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
https://en.wikipedia.org/wiki/Exponentiation#IEEE_floating_point_standard
Most programming language with a power function are implemented
using the IEEE pow function and therefore evaluate 00 as 1. The
later C[40] and C++ standards describe this as the normative
behaviour. The Java standard[41] mandates this behavior. The .NET
Framework method System.Math.Pow also treats 00 as 1.[42]
I understand that the question is open mathematically, but this
has been settled already. Please let's focus on something that
provides value.
