On Saturday, 19. January 2013 20:41:32 Denis Kasak wrote: However, if
the same function was given to you as an infinite list of tuples of (x, f(x)) you would need to do an infinite number of steps just to compute the antiderivative, much less prove anything about it.
An if the function is given as rows in a table (discrete, finite) then I can compute the derivative by just looking at two successive values, however for the antiderivative I have to look at all values between the lowest possible x and the running x. If the function is discrete but has no lower bound for x, then I cannot compute an antiderivative at all, at least not one which will be correct for any x. I wrote an antiderivative function for discrete values and ended up passing it a lower bound for x. IIUC then there is no way to avoid this. Is this about right? It is still somewhat strange. For a discrete function f(i) I can compute the definite integral F(b) - F(a) but I cannot compute F(a) or F(b) themselves. Right? -- Martin