I regret losing my "1000th" post status on this response. Anyways, this response is regarding your first paragraph on your response. I could not have written an infinite amount of 9s, or 0s, which is why I used the "..." to abbreviate everything. The "..." symbol expresses an infinite number, not a non-infinite number. Everytime you see the "...," just visualise an infinite amount of numbers after it.

By the way, in one of my earlier posts in this thread, I wrote an extremely long post, which consisted of thousands of 0s. It mainly served as a joke, but "SOMEONE" had to edit it for "READABILITY." Once this thread dies, I'm rediting it to what it was before.

Oh, okay. Thanks. Doesn't change my explanations at all, though.

Alex, what they mean is, you can't say 1.000...382094832094 because that implies that the "..." is not infinite. If there are numbers at the end, then "..." has a value that is countable, no matter how many numbers you stick in there. Once again, the easiest way to try and disprove 0.999... is not the same as 1 is to find a number between the two. Only problem is, there are no numbers between the two. Therefore ...

Ok then, how about this: what does X equal in the following equation: 1 x = ----------- 1-.999...

There's no such thing as an infinitesimal in the everyday real numbers - so "those numbers" after an infinite number of zeros really don't exist as unique numbers. You can probably make up a system where things are different, but it's really not the system that people use.

Think about it this way: If 1.2 means "1 + 2*10^-1", then what does 1.000...0002000... mean? 1+2*10^-infinity?

But, 10^-infinity would be understood to mean the limit of 10^-x as x goes to infinity, which is just *zero* - not a "really small number". Then even "1.00...00200..." still equals 1.

Well, what else could I have done? I couldn't have kept on typing. I needed an abbreviation. I don't know what else I could have done. I could have put a (to infinity), or a --->, or I could have just kept on typing. Just pretend there is an infinite amount of numbers where the .... is.

Well, if my explanation didn't work, I don't know which one will. The truth is out there somewhere. It definitely has an answer.

Oh wait, I understand now. At first, I thought you didn't know what my "..." referred to. You are stating that the numbers after the "..." don't exist, because there is an infinite amount of numbers before them. Okay, I understand that. But, they do exist, in a weird way.

I feel that I know the answer (which is ...0.999... Does not equal to 1). The only problem I am having is writing it down in a way that everyone else understands.

I can't help but have my common sense take over on this one, rather than a complex system of mathematical equations. I just look at the number, and see it's different than 1 in the fact that it looks lesser. Look at it, it's just not whole. It's missing something. It's missing such a small number that would have made all of those 9s into 0s. How small? That's impossible to know.

...0.0001... Is indeed a small number. It is impossible to know how small that number is. But because it exists, it does not have a value of 0, but the closest thing, next to 0, which is still enough of a value to make ...0.999... lesser to 1. Yes, I know about the whole "..." flaw thingy. I'm not going write an infinite amount of numbers, so I am using "..." as an abbreviation. And yes, I understand that you think the number 1 doesn't exist because of the infinite amount of 0s before it. There is no end to the number, but that stupid 1 still has a value, that spreads evenly throughout the entire number.