It is

This function is continuous only at the point *x*=0. Why? Well, it's certainly
not continuous at any other point, since if , then by taking a
sequence of rational numbers converging to and then a sequence of
irrational numbers converging to , you can see that
doesn't exist. But why is *f* continuous at 0? We know that *f*(0)=0 from the
definition. We also have that for all
*x* (since *f* is always either *x* or -*x*). Since , it follows from the pinching (or sandwich)
theorem that . Since this is *f*(0), this means that *f*
is continuous at 0.

Mon May 5 12:53:33 CDT 1997