I had a debate with an unbelievably stupid American Jew some years ago – one called Mark Chu Carroll.  (http://scienceblogs.com/goodmath/2010/02/04/so-remember-back-in/)

“You can’t traverse that subtree to infinity! You just can’t” claimed Carroll. 

and in the next breath:

“1/3 = 0.333…”

Well, the crank no longer accepts comments on his blog but the following link refutes the idea that real numbers are well defined:


And the following link provides a proof for simpletons that 0.999… is NOT equal to 1:

The fallacy that 1/3 = 0.333… is debunked, and hence the claim that 0.999… and 1 are the same falls.