Inconsistency

[Tim Wessman]

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.