No.Originally Posted by Brad0407
For one, you're implying that the '1' in the answer will be at the end - but the end never comes! The number of decimal places you're representing is infinite. Meaning, there is no limit or end to it, so no place to put your one.
The issue at hand for the post you're refering to claimed (correctly) that:
1) Between every two rational numbers, there is another rational number, and
2) Since there is no number between .9999... and 1, they are, in fact, the same number.
Finding a difference (subtracting) between two numbers is a good way to show they are not equal. So, for the sake of argument, let's pretend your 'calculation' above is valid:
Assume: 1-.9999.... = .0000...1 (A string of infinite zeros with a one at the 'end' - the infiniteth decimal place?)
I'll represent .000....1 as 'd' for the remainder of this post for two reasons:
1) To shorten it
2) It makes me ill
d's construction implies that it is the rational number with the smallest absolute value. I'm not going to get into it here, I can only take so much fake math in one day.
From here we can take a number of paths, but here is the quickest (and most fun):
If d is a rational number, and 0 is a rational number, then one of two things is true:
1) There is a number between them.
2) They are equal.
Since d is the rational number with the smallest absolute value, it is the closest to 0, which implies that there is no number between d and 0 (since if there were, it would be the number with the smallest absolute value). Since there is no number between 0 and d, they must be equal!
So, unfortunately, your post is not only wrong, but even if it were right, it would be wrong.
Note: This is not a flame. The infinite and its consequences are thing to get your head around. I'm just trying to explain a little of it.