Date: Nov 13, 2012 1:34 PM
Author: Joe Niederberger
Subject: Re: How teaching factors rather than multiplicand & multiplier<br> confuses kids!
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 ;-)