Zach’s strange fractional part problem
Tonight, I’m going to be working on an interesting problem that Zach posted to the UHME mailing list. Apparently, he had asked it earlier, and no one attempted it. I feel up to it, after a semester of real analysis, using Rudin’s horrible book. The experience had to be good for something 
Let
be the function defined by the rule
where
denotes the fractional part of
. Determine, with proof, the exact value of
Possibly relevant posts:
- Bessel Families and Frames (10/5/2005)
- Upcoming analysis test (3/27/2005)
exists if 
continuous and 
B.V. (3/17/2005)