MDMAlliance said:
Soleron said:
MDMAlliance said:
Either way, 0.999... is not the exact same thing as 1 due to the fact that it is created by something of infinite "additions." 1 is 1, 0.999... is not. It's the same logic as there's no "biggest number" so therefore infinity isn't the same thing as the "biggest number" because it doesn't exist.
|
It's not created by infinite additions. It's a fixed object with certain properties. Everything we do to test those properties (addition, multiplication, comparison) shows it is indistinguishable from 1. And the best way of thinking about it is that the number '1' has two valid decimal representations, being 1 and 0.999...
|
How is 0.999... a fixed object? Is there some way you're getting 0.999... that I do not know of?
Are we talking about two different 0.999...'s because I don't think it would be a fixed object.
If we talk about 1/9 * 9 or 1/3 * 3 (or whatever else way people use to get 0.999 and 1 being the same thing), to some extent I agree that those two numbers are representing the same thing. I do not agree, however, that 0.999... as an infinity is 1. |
It's fixed because it is the sum of an infinite convergent series, which I've already told you equals a fixed point. It doesn't approach 1. It only approaches 1 if you count a finite number of the terms .9 + .09 + .009... But when you count an infinite number of 9s, and find their sums, (which is what .9999 represents) then you actually reach the number 1.
