I view this as an artifact of our use of base 10. So, if we were to use base three, 1/3(in decimal) is 0.1. And in base 3,

0.1+0.1+0.1=1

That said, you get the even more counter-intuitive proposition: 0.222222... = 1 in base 3.

I think the whole problem comes out as there is no way to represent the number closest, but still less than 1. The number exists, but our methods of representing numbers is incomplete.

Why would someone think that .9 no matter what else comes after would magically change to 1.0? .9 is .9 and even an infinite amount of 9s will not change the value of that first 9!!! Therefore .999 does not equal one, it is just close. And can an infinite amount of 9s or anything for that matter even exist?

I'd like to point out a rather fundamental flaw with your "proof".
Let x=1 and y=.9999...

Now I need to remind you of a basic identity property that any number minus "itself" equals 0.

SO, x-y 0

In your older post you said the following:

"Let me guess: the average is .99999...05? So after this infinite list of 9s, there's the possibility of starting up multiple-digit extensions? Doesn't that just raise the obvious question: What about .9999999...9999999...? Namely, infinitely many 9s, and then after that infinite list, there's another infinite list of 9s? How, exactly is that different from the original infinite list of 9s? If you saw it written out, where would the break between the lists be?"

The same applies to .000....000... The fact is that it IS infinite, but there is something at the end. And infinitely small number does not equal one and further more, adding this infinitely small number to 1 would make it greater than one, but adding it to .999... would make it 1! You cannot argue that it does not exist due to the same logic you are using to say that it is infinitely close to 1. Close does not mean equal.

Matt, what is this "something at the end" you speak of? You do not say what it is, nor do you do any calculations to demonstrate the properties you assign to it. You provide no evidence whatsoever that it exists at all. In other words, you're just like that chicken who runs around claiming that the sky is falling.

I suggest you go to Wikipedia and read the articles there about "Real Numbers" and "0.999...".

Also, if you deign to reply at all, show me your calculation of "1 - 0.999... =". And no, you are not allowed to replace 0.999... with "0.999...9" or similar. The moment you do so, you admit that you have to lie and cheat to prove your case.

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