Not at all. Go to altavista (http://altavista.digital.com) and search
for "space filling curves". There you will find ways to squeeze an
infinitely long 1-dimensional curve into a finite 2-dimensional space
(like a square). Although this doesn't put *every* point on the curve
infinitely close to every other point, it does put infinitely many
points at arbitrarily large distances along the curve, arbitrarily close
to each other in the square. This is just intended to give you an
"intuition" about how you can fold up a dimension to do the things
described previously.