Re: __builtin_cpow((0,0),(0,0))

[Gabriel Dos Reis <gdr at integrable-solutions dot net>]

Paul Schlie <schlie@comcast.net> writes:

[...]

| > You've transmuted the function x^y to the function x^x which is a
| > different beast.  Existing of limit of the latter does not imply
| > existance of limit of the former.  Again check the counterexamples in
| > the message I referred to above.
| 
| Thank you. In essence, I've intentionally defined the question of x^y's
| value about x=y->0 as a constrained "bivariate" function, to where only
| the direction, not the relative rate of the argument's paths are ambiguous,
| as I believe that when the numerical representation system has no provision
| to express their relative rates of convergence, they should be assumed to be
| equivalent;

You're seriously mistaken.  In lack of any further knowledge, one should not
assume anything particular.  Which is reflected in LIA-2's rationale.
You just don't know anything about the rate of the arguments.

| as the question of a functions value about any static point such
| as (0,0) or (2,4) etc., is invalid unless that point is well defined within
| it's arguments path; where if it is, then the constrained representation is
| equally valid, but not otherwise (as nor is the question).
| 
| Therefore in other words, the question of an arbitrary function's value
| about an arbitrary static point is just that, it's not a question about a
| functions value about an arbitrary point which may or may not be intersected
| by another function further constraining it's arguments.
| 
| Therefore the counter argument observing that x^y is ambiguous if further
| constrained by y = k/ln(x), is essentially irrelevant; as the question is

That was just *one* set of counterexample.  It is very relevant to 
the complexity of the issue. 

| what's the value of x^y, with no provision to express further constraints
| on it's arguments. Just as the value of (x + y) if further constrained by
| y = x, about the point (1,2) would be both ambiguous and an irrelevant to
| the defined value of (x + y) about (1,2).

You comparing apple and oranges.  "+" is continuous at any point.  "^"
is not.  That is the core issue.

-- Gaby