Math Facts That'll Make You Say "Wait, What?" #3
Some infinities are larger than others. Georg Cantor proved this in the 1870s and it made several of his colleagues extremely angry. Also: you cannot fold a piece of paper in half more than seven or eight times, and if you could fold it 42 times it would reach the Moon.
Some maths facts are useful. These are not those. They're the kind of thing that makes you stop whatever you're doing and say: wait, is that actually true?
Different Sizes of Infinities
Pick any number. Add 1 to it. Now add 1 again. Keep going. You will never run out of numbers. You will never reach the end. No matter how long you count, there is always one more. This is one of the most important things mathematicians have ever proved. Infinity isn't a very large number sitting at the far end of the number line. It's the fact that the number line has no far end. It just keeps going, forever, in both directions.
And then, once you've got your head around that, mathematics goes and proves there are different sizes of infinity. Some infinities are larger than others. The infinity of all whole numbers is smaller than the infinity of all decimal numbers. Georg Cantor proved this in the 1870s and it reportedly made several of his colleagues extremely angry.
You Can't Fold Paper in Half More Than 7-8 Times
Sounds fake, but it's true. Try it.
Take a piece of paper of any size and fold it in half. Then fold it in half again. Keep going.
You'll hit a wall around 7 or 8 folds, no matter how big the paper is. The thickness doubles with each fold, and by fold 7, you're trying to fold something as thick as a notebook.
But here's the mind-blowing part: If you could fold it 42 times, the thickness would reach the Moon. If you folded it 103 times, it would be larger than the observable universe.
Exponential growth is bonkers... Exponential growth doesn't announce itself. It just sits there, doubling quietly, until suddenly it's reached the Moon. The paper folding thing feels impossible until you try it (and then it feels even more impossible). That's the bit worth holding onto.
Math hides its best moves until you're paying attention.
Previous: Math Facts #2. Every odd number has the letter "e", and there's a number bigger than the universe
Next: Math Facts #4. Why the Romans couldn't write zero, and what it cost them
