Chris wrote:
It may help to think of it this way - I really hope this isn't more confusing.
The number line you usually see contains only integers, whole numbers (and zero). It goes on forever to the positive and negative, and so the number line itself is infinite. That number line has no smaller division than the whole numbers. "…-3,-2,-1,0,1,2,3…"
What Vi is talking about is a number line containing rational numbers - fractions.
That number line also includes the space between the whole numbers, and that space is bigger that you might think it think is, because that space can be infinitely divided. It isn't truly represented by the picture on the page. In fact, if you want to find every possible fraction between "1" and "2" you can't --- that number is infinite as well!
So, (even though a TARDIS isn't infinitely big) it's like someone has a TARDIS (that's the number line), and then sitting inside that TARDIS is another series of TARDISes. (Because there's a new infinity between each whole number set, and each one is infinitely big.)
Because there are so very many numbers between the whole numbers on the number line, the odds are basically infinitely stacked against you ever hitting a whole number.
