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

05222018, 01:13 PM
(This post was last modified: 05222018 03:35 PM by DrD.)
Post: #1




Do you agree: limit(ABS(x)^n,n,∞,1); => undef (Onesided limit: n≥0)
[CAS]
limit(ABS(x)^n,n,∞,1); => undef (Onesided limit: n≥0) Notice also: limit(0^n,n,∞,1); => undef Wolfram, and wxmaxima disagree. 

05222018, 03:30 PM
Post: #2




RE: Do you agree?
Request: better thread title. The actual phrasing doesn't really help to classify the topic. It seems either a generic discussion or one of the late heated discussion.
Wikis are great, Contribute :) 

05222018, 03:38 PM
Post: #3




RE: Do you agree: limit(ABS(x)^n,n,∞,1); => undef (Onesided limit: n≥0)
Is that any better?


05222018, 05:42 PM
Post: #4




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

05222018, 06:36 PM
Post: #5




RE: Do you agree: limit(ABS(x)^n,n,∞,1); => undef (Onesided limit: n≥0)
Limits at infinity should use the syntax limit(expression,variable,inf) for +infinity or inf for infinity, there is no support for sidedlimit at infinity because there is no need to.
As Arno K explained, the limit of abs(x)^n at n=+infinity depends on x, you must make assumptions otherwise you get undef. 0^n is undefined, and 0^n is evaluated before the limit in limit(0^n,n,inf). You can quote to prevent evaluation. Of course that's not really the kind of computation that I run with a CAS :) 

05232018, 12:06 PM
Post: #6




RE: Do you agree: limit(ABS(x)^n,n,∞,1); => undef (Onesided limit: n≥0)
(05222018 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. 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. 

05232018, 04:56 PM
Post: #7




RE: Do you agree: limit(ABS(x)^n,n,∞,1); => undef (Onesided limit: n≥0)
This is the difference between an interactive or noninteractive system. The CAS is noninteractive, it means that you can not ask "Is x>1?" during a computation (like in maxima) and the result must be usable in further computations. In this example, limit would return a piecewise function because the condition can be solved symbolically, but it's not always the case and it would be much more complicated to handle (sooner or later you are faced with combinatoric complexity explosion, especially if you don't have good algorithms to simplify piecewise functions).
Another point to remember is that Giac was primarily designed to do computations that are hard or impossible to do by hand, not these kinds of limits because in my opinion, they should not be solved with a computer, I mean the computer will not give any additional value to what a STEM student should know. Of course, they could happen in an intermediate computation, but then the user should have made appropriate assumptions on the parameter. 

05242018, 09:59 AM
Post: #8




RE: Do you agree: limit(ABS(x)^n,n,∞,1); => undef (Onesided limit: n≥0)
I understand, and my thanks to you, Parisse.
Its very comforting to 'think' that a technology could provide a correct answer for any STEM related problem, but it is equally disheartening to confront the reality that such a technology doesn't exist, at least not in a practical personal singular form. Still, the hp prime, (and your CAS!) is pretty darn cool! I have enjoyed using this device, nearly every day, for several years now. It's the best dollars I have ever spent on anything similar, and no end in sight. So ... thanks for that, too! Dale 

« Next Oldest  Next Newest »

User(s) browsing this thread: 1 Guest(s)