Paul Schlie <[EMAIL PROTECTED]> 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
