Mathematics, philosophy, programming, in-line skating, and everything in between. More about me…
Our long journey through the infinite lands is coming to an end. What end is there to infinity, you ask? I’d have to put on a theologian’s hat to answer that. But as a mathematician, I can answer a question much more daring: what end is there to infinities?
Can there be any fact more shocking than that there are two infinities, one bigger than the other? Well, take a guess… But to crack the mystery underlying the existence of two different infinities, we first need to learn a little more from set theory… Monkeys, sheep, and leopards return!
Let’s challenge our notion of infinity by stating a downright crazy idea… and then proving it beyond any doubt.
We know that the natural numbers 1,2,3,… go off to infinity. But what happens when we consider negative numbers -1,-2,-3,… as well? How many numbers do we get? And what about fractions? Do we have multiple infinities?
Let’s quickly recap the most important (and weird) properties of the “natural numbers infinity” we call <$\aleph_0$>.
Back in spring I started a series on interesting mathematical topics for the layman. Now I’m back with some fresh stuff. I’m still aiming to explain thrilling areas of pure mathematics to a non-mathematical audience.
Are there more even numbers than odd numbers? How much can we take away from infinity to keep it infinite? And how much is “ten times infinity”? Is it more than “twenty times infinity”? Do these questions have a meaning at all? Let us delve into the depths of the infinite oceans once again!
Do you know what the largest natural number is? Where do the borders of the infinite realm lie? And how many monkeys does it take to write the complete works of Shakespeare? Come hither, ye finite mortal, and behold the glory of eternity that men have created in their minds!
Are you a non-mathematician? Do you want to know a little about interesting mathematical phenomena? I am starting a series of articles on selected mathematical topics. I am going to explain them very simply and comprehensibly. No prior knowledge of higher mathematics will be needed. Today, we are going to talk about sets and their sizes. In the next article, we will use this knowledge to understand the mightiest beast itself – infinity.