x = 0.9999...
10x = 9.999...
10x = 9 + 0.999...
10x = 9 + x
9x = 9
x = 1
x = 0.9999...
2x = 1.9999...
2x - x = 1
x = 1
"It's much more intuitive that 10 * 0.9999... = 9.9999... than that 2 * 0.9999...= 1.9999..."
x = 0.999...
to
2x = 1.999..
If you see an 8 it’s because you didn’t carry the 1. Keep going.
Another way to think about it is that you have n digits, and I’m using the n and n + 1 digit at the same time. But since n goes to infinity, +1 hardly matters.
Write
0.9
+ 0.9
—————-
1.8
Where people keep getting tripped up is thinking you can stop when you get tired, or die, or when the universe ends in heat death. You don’t get to stop. You never get to stop. It’s nines all the way down.