Now keep extending the 9’s. You have to carry a one, so fix the carry and then add more nines.
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.
It’s less intuitive, but still relatively straightforward from performing the “long” multiplication. You do need to convince people that the “8 at the end“ is irrelevant, however.
You need to convince people there is no 8 at the end because there is no end.
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
Now keep extending the 9’s. You have to carry a one, so fix the carry and then add more nines.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.