Philosophy of Mathspeaking topic
The numbers between 0 and 1 outnumber all the integers put together. Both collections are infinite, but one is a bigger infinity than the other. If even infinity has a class system, is there such a thing as the biggest infinity?
— Cantor's diagonal argument
practice with this topic
Set the timer (5-30 min), take 20 seconds of prep if you like, start talking. Jot your thoughts onto the sticky-note board.
similar topics
- Why does intuitionism, the austere school of mathematics, reject proofs by contradiction, and what does it even mean to claim that something exists?
- How do fractals and the Mandelbrot set, where infinite complexity springs from a simple formula, open up the question of whether infinity can hide inside a finite rule?
- A group of people is discussing its average wealth. A billionaire walks in and the 'average wealth' suddenly makes everyone a millionaire, though nobody's pocket has changed. Why is the average so bad at describing the majority?
- Look at stars scattered randomly on a page and you will always see clusters and patterns. But a truly random distribution looks exactly like that: clumpy. If it were evenly spaced, we would call it fake. Why isn't randomness orderly?
- Break a stick at two random points, and the chance that the three pieces can form a triangle is only one in four. Intuition says fifty-fifty, but geometry is strict: if one piece is too long, the triangle collapses. Why does randomness so often produce a shape that will not close?