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Inconsistency
09-02-2015, 11:51 AM
Post: #1
Inconsistency
Hi all

With the current firmware (2015 6 17 (8151)) I get the following results in CAS-mode:

0/0 = undef
1/0 = +- \infty
sin(0.5)/0 = +Inf

as well as
1/\infty = 0

In each of the first three cases I get a different output. In addition, the second and third result is simply wrong. If I wanted a limit I'd write a limit. My students don't know yet about limits, all they know is that division by 0 is not defined. So it will be hard to explain to them what this output is suposed to mean.

I also dislike the fourth result a lot. Infty is surely not a number I can just use for division. I think the calculator should be much more strict here especially for the students. However, one could argue differently here.

Bests.
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09-02-2015, 02:45 PM
Post: #2
RE: Inconsistency
(09-02-2015 11:51 AM)whilealive Wrote:  With the current firmware (2015 6 17 (8151)) I get the following results in CAS-mode:

0/0 = undef
1/0 = +- \infty
sin(0.5)/0 = +Inf

as well as
1/\infty = 0

In each of the first three cases I get a different output. In addition, the second and third result is simply wrong. ...

"Simply wrong": no. Ever since the HP implemented the brand-new IEEE standard for Infinity and Not-a-Number in the HP-71B, HP's most advanced calculators have all returned results like these, because that's what the standard specifies.

Examples on the HP 50g in exact mode:

0/0 --> ? (called NaN on the HP-71, and "undef" on Prime)
1/0 --> Infinity
0.5/0 --> Infinity
1/Infinity --> 0

The IEEE standard (IEEE 754) specifies that division by zero should return infinity: https://en.wikipedia.org/wiki/IEEE_float...n_handling

<0|ΙΈ|0>
-Joe-
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09-02-2015, 04:12 PM (This post was last modified: 09-02-2015 04:23 PM by Tim Wessman.)
Post: #3
RE: Inconsistency
Hello,

One other thing I'd like to point out here is that +-infinity you are seeing as well isn't by accident. That is how the calculator represents "complex infinity". For example:

sin(1/2)/0 http://www.wolframalpha.com/input/?i=sin%281%2F2%29%2F0

You'll note how mathematica returns complex inf as well for these types of situations. In terms of what to explain to students, they really can grasp the idea that "this means the graph shoots off upwards from one side, and downwards on the other". It provides nice information as to what is happening at that spot and can really help them join some concepts together.

Also note that sin(.5)/0 will behave slightly differently then sin(1/2)/0. The latter will give you a complex infinity while the former behaves as Joe mentioned because it is a "approximate numeric value" at that point and not an exact symbolic.

As for being "stricter", the calculator is being about as strict as you can get since it is following the defined rules with exactness (maybe a different set of rules then the ones you were expected, but I'd argue the "most correct" ones). The point of view as to what those rules should be of course are open for debate.

As a side note, I think every CAS system will return 0 for 1/inf.

TW

Although I work for the HP calculator group, the views and opinions I post here are my own.
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09-03-2015, 02:17 PM
Post: #4
RE: Inconsistency
Thanks for the quick replies. This helps me a lot.

Quote:"Simply wrong": no. Ever since the HP implemented the brand-new IEEE standard for Infinity and Not-a-Number in the HP-71B, HP's most advanced calculators have all returned results like these, because that's what the standard specifies.

Well, I don't know if following a floating point standard is some reason for correctness. But I guess we are talking about two different types of correctnesses here. Of course I can accept the implementation of the standard even though it will be hard to teach the pupils why their device does such "very bad" things as dividing by 0. I'll do my best.
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