h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

It is true that there exists no division to find pi. But consider what pi represents. The circumference of a circle (unless I'm way off the mark). That circumference contains infinite points within points and I would assume that means it cannot be nailed down by any absolute value like a fraction would give.
If we then examine a number line, I think the same logic could be applied. If one agrees that a number line can continue forever in the positive and negative direction, then wouldn't that infinity be similar to one of a circle? Both do not end, but does this mean that positive will become negatives and eventually become positives again? Have I gone too far? I'm going to go get some sleep.

The problem is in defining infinity. It is true that the set of all rational numbers is infinite and so is the set of all irrationals. However, it can be shown (by Cantor's Diagonal Argument) that the set of all irrationals is a "larger" infinity than that of all rationals. The problem is, if I remember correctly, that there is no way of saying HOW large the set of irrationals is, as demostrated by the unprovable Continuum Hypothesis.