3 ms·

or, x = 0.9999... 10x = 9.999... 10x = 9 + 0.999... 10x = 9 + x 9x = 9 x = 1 Presented slightly more clearly https://en.wikipedi

• hinkley 7y ago
  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
  • moonchild 7y ago
    It's much more intuitive that 100.9999...=9.9999... than that 20.9999...=1.9999...
    • ColinWright 7y ago
      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..."
  • champagneben 7y ago
    How do you jump from x = 0.999... to 2x = 1.999..
    • saagarjha 7y ago
      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.
      • hinkley 7y ago
        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.
    • hinkley 7y ago
      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.