At your age (from your profile), it is most likely that you have only been introduced to a relatively small subset of mathematical ideas. The same is true for me too, in a relative sense - I am much older than you, and certainly don't claim to be a mathematician - there is vast amounts of stuff I don't know. But that doesn't stop from having an interest, but it doesn't mean that I practice what I have an interest in.
I guess the reason I don't see things like x/0 as a "profanity" is because maths has a term for these things - this particular one is infinity, inverse is x/infinity = 0. The maths constant
(a complex number) is defined as being
There is a whole branch of maths that deals with complex numbers.
The thing is, programming languages operators at least, work with real values, unless they are overloaded. But some of the math library functions (am thinking the trig functions) return things that mean NaN (not a number) and infinity. I presume that these are mainly used to detect errors. Then there are libraries that will actually do complex math, but I haven't bothered to see if they can do calculus with them or not. I haven't tried this, but I have a vague idea that the compiler will return NaN or other values for ordinary statements as well. Like if one does this:
double a = 1.0 / 0.0;
It might be possible to compare the value of variable a with NaN. I am not sure, I don't normally mess with this sort of thing.
A remarkable thing about Euler's (pronounced "Oiler" - he was an Italian) equation is that it provides a link between the most important constants in maths - 0, 1, e, pi, i. I paraphrased that from Dunham's book.
The equation, before Mats
intentionally abused :+D it for the purposes of this topic, is:
|e i pi + 1 = 0|
Any way, I have to go now, hopefully I have provided some food for thought !!
EDIT: Perhaps I should have said that 1/infinity is infinitesimally close to zero. But x/0 is infinity though - do a graph of a/x where a is any constant value. The smaller x is, the bigger y is.