Am 18.11.2013 10:50, schrieb quasi: > Robert Crandal wrote: >> >> Suppose I have the following X-Y data set: >> >> X Y >> -- -- >> 0 1 >> 1 1 >> 2 2 >> 3 3 >> . . >> . . >> N N >> >> Can this be represented with a math function? >> >> (Only consider positive integers >= 0) > > It's already a function since for each x in the domain, there > is a unique y. > > Presumably you want a "formula". > > The function f defined on the set of nonnegative integers > by the formula > > f(x) = ((x-1)*(((2*x-1)/abs(2*x-1))+1)/2)+1 > > is not pretty but it works.
Instead of making complicated gymn with abs(x) function by expressing the sign(x) function via x/abs(x), x!=0, in most cases it easier to take the most elementary continuous piecewise linear function with a kink, the min/max functions
In the present case a very simple function is
y = max(1,x)
But of course, pointwise fit an analytic function will be possible too where sinx(x/pi)/x can be used to fit values 0 at the integers !=0 and an exceptional value of 1 at x = 0.