0.999... = 1
This is heavily disputed in mathematics, and I wish people would realize that it really is true. There are cooler things such as how the sum of the natural numbers (1+2+3+...) equals -1/12, but people don't even agree that 0.999... = 1. I'm just hoping that this thread will open your eyes if you didn't already believe that 0.999... = 1. My aim is to have everybody who sees this answer yes in the poll. If you have any arguments or questions, or have some other comment, please reply to this. If you answer the poll with "no," please state why you disagree. I'll now provide 5.999...
common proofs that 0.999... = 1:
Proof #1:The proof goes like this:
x = 0.999...
10x = 9.999...
9x = 9.999... - x
9x = 9 (since x = 0.999... you can substitute 0.999... for x)
x = 1
Because x = 0.999... and x = 1, 0.999... = 1.
Proof #2:This is a very common proof:
1/3 = 0.333...
1/3 + 1/3 + 1/3 = 1
0.333... + 0.333... + 0.333... = 0.999...
Therefore, 0.999... = 1
Proof #3:This is basically the same thing
1/9 = 0.111...
1/9 * 9 = 1
0.111... * 9 = 0.999...
Therfore, 0.999... = 1
Proof #4:This one uses more logic, and less math:
There is no number between 0.999... and 1. Any two numbers with different values have a number in between them. Between 0 and 1 is 0.5. Between 0.5 and 0 is 0.1. Between those is 0.000001. Between those, there is 0.00000000000000000003403, and this goes on and on. There is no number between 0.999... and 1. If you add another nine, it's still infinite nines and doesn't change the value.
Proof #5:The difference between 0.999... and 1 is 0.
If you take 1 - 0.999... you get 0.000...1, but there's infinite zeroes, so you never get to the final 1. Therefore, 1 - 0.999... = 0.
Proof #6:99.999% of mathematitions agree!
@tauloverEDIT: fixed some typos.