Evaluating Undefined expressions?

[Spybot]

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!

[Joe Horn]

(11-06-2015 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.

[Spybot]

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?

[parisse]

CAS is correct.

[retoa]

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

[Han]

(11-06-2015 08:38 AM)retoa Wrote:  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

I think you missed the absolute value signs.

[Spybot]

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!

[Han]

(11-06-2015 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.
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!

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.

[retoa]

(11-06-2015 01:59 PM)Han Wrote:  

(11-06-2015 08:38 AM)retoa Wrote:  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

I think you missed the absolute value signs.

You are absolutely right !!!

[Han]

(11-06-2015 09:58 PM)retoa Wrote:  

(11-06-2015 01:59 PM)Han Wrote:  I think you missed the absolute value signs.

You are absolutely right !!!

I see what you did there.