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.
Joe N said: >Nice trick though.
Sorry - I should've also noted that according to the mathematicians, you would need to lift your pencil uncountably many times along the top two quadrants to skip over all the "gaps" left by the irrationals...
Better start with the bottom two quadrants> Oops! Similar problem, but infinitely more manageable ;-)