Mathematics, philosophy, code, travel and everything in between. More about me…

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Infinity

Infinity of Infinities

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?

The Set of Subsets of a Set

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!

The Bigger Infinity

Let’s challenge our notion of infinity by stating a downright crazy idea… and then proving it beyond any doubt.

September 29, MMXI — Mathematics, Maths For Normal People, Infinity.

All The Numbers In The World

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?

September 22, MMXI — Mathematics, Maths For Normal People, Infinity.

Aleph-Null Bottles Of Beer On The Wall

Let’s quickly recap the most important (and weird) properties of the “natural numbers infinity” we call <$\aleph_0$>.

September 15, MMXI — Mathematics, Maths For Normal People, Infinity.

Reintroducing Maths For Normal People

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.

September 12, MMXI — Mathematics, Maths For Normal People, Infinity.

On The Finiteness Of Life Experience

There’s a great new comic at Spiked Math: It’s a small world (after all). Be sure to check it out even if you are not a mathematician. Using mathematical reasoning, the comic asserts that the number of ways you could lead your life is finite, in other words, there is a limit to what you could do in your life. I strongly disagree, and I can disprove this assertion using the very same tool: mathematics :-)

May 26, MMXI — Mathematics, Infinity, Philosophy.

Infinity Plus Three (Maths For Normal People III)

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!

Of Macbeth And 100,000 Monkeys (Maths For Normal People II)

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!

My Cardinal Is Bigger Than Yours (Maths For Normal People I)

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.