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An infinite number of mathematicians enter a bar in Australia. The first one orders a beer. The second one orders half a beer. The third one orders a fourth of a beer and so on. The bartender is about to fill up two glasses of beer when one mathematician interjects: ``So what about an `infinite set'? Well, to begin with, you should say precisely what the term means. Okay, if you don't, at least someone should. Putting an adjective in front of a noun does not in itself make a mathematical concept. Cantor declared that an `infinite set' is a set which is not finite. Surely that is unsatisfactory, as Cantor no doubt suspected himself. It's like declaring that an `all-seeing Leprechaun' is a Leprechaun which can see everything. Or an `unstoppable mouse' is a mouse which cannot be stopped. These grammatical constructions do not create concepts, except perhaps in a literary or poetic sense. It is not clear that there are any sets that are not finite, just as it is not clear that there are any Leprechauns which can see everything, or that there are mice that cannot be stopped. Certainly in science there is no reason to suppose that `infinite sets' exist. Are there an infinite number of quarks or electrons in the universe? If physicists had to hazard a guess, I am confident the majority would say: No. But even if there were an infinite number of electrons, it is unreasonable to suppose that you can get an infinite number of them all together as a single `data object'.''
