I recently ran into the phenomenon of Cantor Cranks. These people can’t wrap their head around the concept of infinity and the fact that it’s very,very not intuitive. Like the amount (cardinality) of natural numbers (1,2,3,4,5…. and so on) and the amount of even numbers (2,4,6,8,10…. etc.). As is bijective, the logical conclusion is that every natural number can be linked to an even number – to infinity, and so there are as many natural numbers as there are even numbers. ‘But…but… you skipped half of the numbers!’
It can even get worse.
Georg Cantor proved (with the diagonal argument) that there are more real numbers than natural numbers. The cardinality of real numbers (aleph one) is bigger than the cardinality of natural numbers (aleph zero). A very elegant proof (I’ll show it in another blog post, but it’s in the video as well) that however tickles some people’s anti-logic feelings. ‘But… but…. there’s only one infinity!’
Here’s a video made by Numberphile about infinities. To see how un-intuitive infinities are. If you’re no crank.