About the best you can do is to choose two sequences of numbers to map 0 and 1 to, and use the identity for everything else. For example, f(1/3^n) = 1/3^(n+1), f(1-1/3^n) = 1 - 1/3^(n+1), both for n>=0, all other f(x) = x. Franklin T. Adams-Watters -----Original Message----- From: lkmitch@gmail.com More of an intellectual curiosity question than anything useful. Is there a "nice" function that is one-to-one and continuous that maps the closed interval [0, 1] to the open interval (0, 1)? Ideally, such a "nice" function would be not a piecewise function or a power series and something that could be implemented with standard library functions. If such a thing doesn't exist, is there at least a "not nice" function that is one-to-one and maps the intervals? If not, why not? Thanks for any pointers or wisdom, Kerry Mitchell -- lkmitch@gmail.com www.fractalus.com/kerry ________________________________________________________________________ Check Out the new free AIM(R) Mail -- 2 GB of storage and industry-leading spam and email virus protection.