Re: Cantor Confusion

David Marcus writes

....

>It is true that k is not continuous, but it is a perfectly valid
>function. Do you know the definition of "function"?

Doubtless you lot have some legally watertight definition. As far as I
am concerned, a function is a formula that provides a value for a given
input (or inputs, in a multidimensional situation).

Ah, you are at least a hundred years behind the times. No, a function is
most definitely not a formula. A function is a rule which assigns, to
each of certain real numbers, some other real number. For example, the
rule that assigns to each number a the number 0 if a is irrational and
the number 1 if a is rational is a function, but you will have a hard
time coming up with a formula (nor is a formula required).

Thanks for that, but actually it appears "formula" has a technical meaning for you. rule and formula are synonyms for me.

Well that is undoubtedly the answer to the question. Why doesn't the
Taylor expansion work might be a better way of phrasing the question?

An interesting question. It turns out that the behavior of the function
for complex values of x prevents the Tayor series from working for real
values.

OK, thanks, I will look that up I guess. Bit it is odd superficially
in that e(-1/x^2) is super smooth with all its derivatives etc.


You might enjoy looking at the book Calculus by Michael Spivak. I'm sure
that it explains Calculus in a way that is very different from how you
learned it.

Thanks I might well do that.

--
Andy Smith
.