This is the first part in a series of four videos that Simon wants to record about Infinities Driving You Mad. Don’t worry, you won’t go mad just yet! The first video is about cardinal numbers, enumerable infinite sets and Aleph Null. Simon also shows Georg Cantor’s proof of why real numbers are not enumerable and explains what Continuum Hypothesis is about.
Earlier Simon told me about the Continuum Hypothesis, that states that there’s no infinity between the size of the natural and the real numbers: “There is no proof for it. It’s what I like to call a superposition problem: the answer is both yes and no. We do know the answer but the answer is that we son’t know the answer. You can choose what you want the answer to be and the mathematics will still be consistent!”
Warning: The next part may make your mind overheat as Simon will hop over to ordinal numbers.