[CAS] Integrals

[AlexFekken]

(09-29-2017 01:17 PM)DrD Wrote:  However, the command sent to the tool was to integrate over the continuum. It can't, and that should be the answer.

Thanks for your detailed response and my apologies if I sound over the top. I see a lot of these types of discussion being based on a misunderstanding or misrepresentation of the underlying mathematics and so I try to correct and explain, usually from a mathematical (abstract if you like) viewpoint. In that sense the quote above is where I disagree with you and have to say "it depends".

If it is your choice (!) that all expressions involving a singularity or infinity should have an undefined result then I can at least agree that this might provide a consistent framework that could be the basis for a CAS or numerical tool. And presumably it would make life easy (or easier) for people like Parisse.

But as soon as you expect the tool to be able to handle some types of "singular behaviour" without automatically producing an "undefined" result (and most people apparently would expect that, or "infinity" would not even exist as a possible value) then you are opening the door to the sort of discussion that we are having here and you need to motivate when and why a result should be "undefined", "infinite" or something else.
This is why I mentioned the integral of |x|^(-1/2), which by your logic (if I understand it correctly) should also be undefined because the function is also unbounded near zero, just like x^(-2). Of course every mathematician would disagree with you on that...

NOTE: I have assumed that by "integrate over the continuum" you mean "integrate an unbounded function", or one that "goes to infinity", and not "integrate over the interval of all real numbers".