Do you agree: limit(ABS(x)^n,n,∞,1); => undef (One-sided limit: n≥0)

[DrD]

(05-22-2018 05:42 PM)Arno K Wrote:  For x>1 the limit is infinity, for x=1 it is 1 and for 0<=x<1 it is zero. With assume(x>1) your limit returns inf, as expected, and, when I do assume (x<1) and additional(x>0), it returns 0, so undef is reasonable.
Arno

My point:

Accepting limit(ABS(x)^n,n,∞,1); => undef; as a reasonable answer, (and Parisse has explained that it IS the result he wants to report here), that,
after citing three valid definitions, a result "undefined" could still be termed "reasonable:" (defined ≠ undefined).

A result something like one of these would seem to have less weakness than "undef," because limit(ABS(x)^n,n,∞,1) has definite solutions:

[[0≤x<1,0], [x=1,1], [x>1,∞]];
or: indeterminate ( could be something like: ind assume(x..?) )
or: parametric
... etc.