Quote Originally Posted by Magnus213
I still don't like this. y and y1 will continually subdivide and approach 1 and all that, but "and they're both 1" and "we both end up with 1" don't prove that they become one. The number will just get infinitely close to 1 and infinitely longer on paper, but never actually get there.

I feel like something fishy is going on with the numerical proof as well. Let's assume that n = 6, so x = 0.999999. Pretty close to 1, clearly not infinitely close, but let's go with it.

x = 0.999999
10x = 9.99999 (notice that you lose a decimal place value)
10x - 0.999999 = 9.99999 - 0.999999 = 8.999991
9x = 9(0.999999) = 8.999991 =/= 9
x =/= 1

I don't see how you can fundamentally say that two distinctly different numbers have the same value.
For part A, think in terms of limits, not any finite point in time. You cannot "freeze" the process at any point and check to see if it works.

Part B, same thing. the 9s never stop repeating (hence the 3 dots)
10x-x = 9x, not 8.999x

Good points though - but let me assure you that this stuff is true. I did NOT just create this proof, its a "well known fact". Juts check online or ask any math professor.