♾️ Infinity
How it works
Infinity is not a number. It is the idea of something that never ends — you can never count to it or reach it, however long you go on.
The four parts here are real mathematics. Hilbert’s Hotel is a puzzle the mathematician David Hilbert used in 1924; the pairing idea is how Georg Cantor compared infinities in the 1870s and 1890s.
Four ways to poke at something that never ends.
Is there a biggest number?
Build the biggest number you can. Whatever you make, watch what happens.
Your number
And one bigger
Hilbert’s Hotel
This hotel has infinitely many rooms — 1, 2, 3, 4, and on forever. Tonight every room is full. Can it fit anyone else?
…and the rooms go on forever.
Halfway forever
The frog jumps toward the wall, but each jump only goes half of the way that is left. How far does it get if it jumps forever?
Zoomed in on the gap the frog just jumped into
Same size?
Are there more counting numbers (1, 2, 3, …) than even numbers (2, 4, 6, …)? The even numbers are only half of them… aren’t they? Pair them up and see.