Actually though the blame is on squeak for this one. He did not specify which infinite series between negative and positive infinity he was talking about, and so you assumed that he was talking aleph null class infinity, when really he was talking about aleph one class infinity (which he only later specified).
My father explained the difference between these through the pigeonhole principle, with the Hilbert’s hotel example and also the 99 bottles of beer. Just look those stuffs up. ^_^