In order to make r=0 in the sense given by the equation, you'd need to have compacted either the TV or yourself into a singularity. (Since r is the distance between the two centres of mass) And even then, you'd still be dealing with a finite r (Albeit on the scale of plank lengths)

This has been the only response worth reading so far. I would point out, of course, that narcbery was not concerned with the state of things when r=0, but rather, the state of things as r approaches 0 (GroundControl's response partially covers this, since r is not allowed to arbitrarily approach 0).

narcberry: G, m1, and m2 in the case of you and the T.V. are very very small. Use the radius of a T.V. for r and actually compute the resulting F, and you will find that as close as you can get to the T.V., the force of gravitational attraction between you and it will still be minuscule.

As a side note, every object has a Schwartzschild radius related to its mass, much like a black hole does. What makes a black hole different from other objects is that its physical extent is smaller than its Schwartzschild radius. The Schwartzschild radius of your television set is practically indistinguishable from zero; by the time you got to it, you would be well inside the T.V., and the gravitational field would have dropped off linearly and not, as you suggest, approached infinity.