Gary Tupper writes: >Consider the function: F: y= x^2 if x is rational; -x^2 if x is irrational Appears to be continuous at a single point (0,0) only. Can be drawn without lifting the pencil - as long as the pencil stays still.
Come again? Do you mean -(x^2)? And by "pencil stays still" are you referring to retracing? If we are being that literal how does one get the pencil to go to infinity and back? Nice trick though.