Hi Oleg,

One has to be careful here. The best that mathematics has to say about this is that "In the limit that dx approaches zero, 1/dx approaches ±INF." This is part of the reason that division by zero is undefined. As you approach zero, the value of the reciprocal depends on the side of zero you approach from. Thus, you can not say that 1/0 = INF, since it could just as easily = -INF. NaN (not a number) is an artifact of numeric approximations.

Compare this to multiplication by zero wherein you always get a result of zero, which by definition is "well defined." (Doesn't that just sound circular?)

Now if you want to know where I part company with the theoretical mathematicians, it's when they start talking about aleph_0 and the idea of one infinity being greater (larger) than another infinity. It is my assertion that "greater than" and/or "lesser than" are quantified characteristics or properties and therefore can not be applied to sets which exceed or defy quantification. But that's just my humble opinion.