Evaluating Undefined expressions?

11062015, 04:50 AM
Post: #1




Evaluating Undefined expressions?
Hello!
Working in CAS view I found this weird situation... While evaluating an inequality at X=0, such inequality has an "X" in the denominator, so I expected to get an error message or a zero(false statement)... but instead I get a "one", I assume that it means that the statement is true. I know it can't be true, so I wonder if it is just me getting this kind of result! Spybot. 

11062015, 06:08 AM
(This post was last modified: 11062015 06:09 AM by Joe Horn.)
Post: #2




RE: Evaluating Undefined expressions?
(11062015 04:50 AM)Spybot Wrote: ... I get a "one", I assume that it means that the statement is true. I know it can't be true, so I wonder if it is just me getting this kind of result! It *is* true, because 2+5/0 = infinity, which is > 1. In CAS, that is. In Home, division by 0 yields an error. <0ΙΈ0> Joe 

11062015, 06:28 AM
(This post was last modified: 11062015 04:06 PM by Spybot.)
Post: #3




RE: Evaluating Undefined expressions?
Thank you Joe for the feedback.
The Function App (plot & table) tells me... zero for this inequality is not defined, but CAS view tells me that at: X=0 this inequality is true, and HOME view says "no, it isn't". ...?... So, which one should I trust? Spybot. 

11062015, 07:48 AM
Post: #4




RE: Evaluating Undefined expressions?
CAS is correct.


11062015, 08:38 AM
Post: #5




RE: Evaluating Undefined expressions?
Does it not depend on from where you approach zero?
If you approach zero coming from +1 you get for 5/0 a positive value which then tend to infinity. If you approach zero coming from 1 you get for 5/0 a negative value which then tend to a negative infinity, so 2+(infinity)=infinity < 1 

11062015, 01:59 PM
Post: #6




RE: Evaluating Undefined expressions?
(11062015 08:38 AM)retoa Wrote: Does it not depend on from where you approach zero? I think you missed the absolute value signs. Graph 3D  QPI  SolveSys 

11062015, 07:01 PM
Post: #7




RE: Evaluating Undefined expressions?
Hp Prime CAS; says "zero" make this inequality a true statement, while WolframAlpha doesn't include "zero" in the number line, just like the HP Prime Function App suggests graphically.
Too many contradictions. As Parisse said: "CAS is correct." I also agree with that... I just wish CAS and HOME converge one day in situations like this! Spybot. 

11062015, 08:50 PM
(This post was last modified: 11062015 08:53 PM by Han.)
Post: #8




RE: Evaluating Undefined expressions?
(11062015 07:01 PM)Spybot Wrote: Hp Prime CAS; says "zero" make this inequality a true statement, while WolframAlpha doesn't include "zero" in the number line, just like the HP Prime Function App suggests graphically. I suppose contradictions would be the appropriate term here since it is unclear whether we are working over just real numbers or over the extended reals (i.e. the real numbers extended with \( \infty \)). In the former, undefined would be the correct result. And in the latter, 1 would be the correct result. In Home view, everything is "numerical" in that all terms must be known numerically. Even variables  if they exist, their value is whatever we assign, or 0 by default. As for \( \infty \), that's not a number  it's more of a concept, in my opinion. However, in the CAS view, we are allowed to have symbols (undefined variables) and by extension, the CAS would also be able to handle \( \infty \) in the same manner that it is able to handle the variable \( x \) even if no value is stored. Graph 3D  QPI  SolveSys 

11062015, 09:58 PM
Post: #9




RE: Evaluating Undefined expressions?
(11062015 01:59 PM)Han Wrote:(11062015 08:38 AM)retoa Wrote: Does it not depend on from where you approach zero? You are absolutely right !!! 

11062015, 10:10 PM
Post: #10




RE: Evaluating Undefined expressions?
(11062015 09:58 PM)retoa Wrote:(11062015 01:59 PM)Han Wrote: I think you missed the absolute value signs. I see what you did there. Graph 3D  QPI  SolveSys 

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