After Mark’s thoughts on Hilbert’s Hotel and similar ways of thinking about infinities, I should have reeled off my favourite definition, from Jonathan Swift.
So, naturalists observe, a flea
Hath smaller fleas that on him prey;
And these have smaller still to bite ‘em;
And so proceed ad infinitum.
Hilbert’s Hotel is a better introduction to the idea of working with infinities, and the notion of the countably and uncountably infinite, but Swift’s just, well, sums up the notion of what an infinity is superbly. Better even than the infinite tower of tortoises on which the world stands, alluded to by Stephen Hawking in A Brief History of Time.