Interesting - thanks.  I wonder if the problem is that people try to think of infinity as a number that's just really, really big - bigger than all the numbers.  If you think of infinity as being the biggest thing there is, then you've got a problem.<p>You (and others) are not alone.  Infinity was a major problem for a very, very long time, with many contradictions and paradoxes arising because of insufficiently careful reasoning.<p>Here's another explanation:<p><a href="http://www.solipsys.co.uk/new/CantorVisitsHilbertsHotel.html?HN" rel="nofollow">http://www.solipsys.co.uk/new/CantorVisitsHilbertsHotel.html...</a><p>and here's something some people think of as a paradox:<p><a href="http://www.solipsys.co.uk/new/BallsInBarrels.html?HN" rel="nofollow">http://www.solipsys.co.uk/new/BallsInBarrels.html?HN</a>