There’s no difference between the number 1 and the seemingly smaller number 0.9999… (with 9 repeating endlessly). I used to think that there must be some tiny but key difference, but it turns out there just isn’t any. They seem different and are written differently, but they are the same.
Here’s one proof: Multiply 0.999999… by 10.
Then subtract 0.999999…
The result is 9.
What’s the difference between ten and nine? One.
It’s true that the solution for 10x-x=9 is 1.
So 0.9999… = 1. Weird!