Well, so far I have'nt been able to do this one so any solutions will be new to me!

How do you prove that the Cantor set is nowhere dense?

I suspect I know who's going to come with a quick reply and make this look fiendishly simple!

Just to be clear, anyone who feels the need to chip in with their two cents worth when they don't really know what they're talking about, with things like "it's how we use 'numbers' that makes it 'dense'" or any of that of that meaningless dribble, please save it for another thread! I would like to see genuine solutions to the problem please.