Re: Is recursive periodic function possible?

On Apr 10, 3:43 pm, dillog...@xxxxxxxxx wrote:
hi

Is recursive periodic (continuous) function possible?
f(n)=-f(n-1) is sorta periodic, but obviously non-continuous.
I can't think of one. It seems difficult to bound a recursive function
and make it periodic at the same time.

I think your question is a little vaguely defined. Here is a
continuous recursive function:

f(x) = x if 0 <= x < 1
f(x) = f(x - 1) otherwise

This function is continuous on the interval [0,1].

Or even better:

f(x) = x if 0 <= x < 1
f(x) = 2 - x if 1 <= x < 2
f(x) = f(x-2) otherwise

Is (or at least, should be, if I did it right) and is continuous along
all of R.

.