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Comment by hinkley | Hacker News Reader

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hinkley

Yeah that’s way more complicated than it needs to be and I’m tempted to replace that whole section with:

x = 0.9999...

2x = 1.9999...

2x - x = 1

x = 1

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It's much more intuitive that 100.9999...=9.9999... than that 20.9999...=1.9999...

You've met the formatting limitations. You mean:

"It's much more intuitive that 10 * 0.9999... = 9.9999... than that 2 * 0.9999...= 1.9999..."

How do you jump from

x = 0.999...

2x = 1.999..

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.

Picture an infinite ticker tape in your mind.

Write

   0.9
 + 0.9
 —————-
   1.8

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.

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