You ever see a dog that’s got its leash tangled the long way round a table leg, and it just cannot grasp what the problem is or how to fix it? It can see all the components laid out in front of it, but it’s never going to make the connection.
Obviously some dog breeds are smarter than others, ditto individual dogs - but you get the concept.
Is there an equivalent for humans? What ridiculously simple concept would have aliens facetentacling as they see us stumble around and utterly fail to reason about it?
One way to tell if two numbers are equal is to show there’s no real number between them. Try to formulate a number that’s between 0.999… and 1. You can’t do that.
But between 0.999 and 1 is 0.9999.
If something comes ever increasingly close to, but never physically touches something else, would you say it’s touching it?
0.999… means infinitely repeating 9s. There’s no more 9 to add that hasn’t already been added. If you can add another 9, then it’s not infinitely repeating.
So it never ends, and it stays 0.9… infinitely?
Still not a 1.
It’s an infinite number of nines after the decimal.
Or think of it another way. What number would you subtract from 1 to get 0.999… ? The answer is 0.
let x = 0.999…
so 10x = 9.999…
subtract first line from second:
9x = 9
divide by 9
x = 1
deleted by creator
an asymptote 😎