[split] 0.999... equals 1

[Tiberius]

That is simply a limit.

No it isn't. The series converges to a real number, due to the completeness property of real numbers. For more information, see: http://en.wikipedia.org/wiki/Infinite_se...ent_series

The problem still goes back to any infinite number or series. Infinity is basically a concept and not a real number.

Yes, infinity is a concept; nobody is arguing against that. However, it is a concept that mathematics allows, and has studied at great length. Infinity doesn't need to be a real number in order to exist in mathematics; there are infinitely large sets of numbers (the natural numbers are countably infinite, and the real numbers are uncountably infinite) for example.

1/0.999...=1.00...100...100...1
That answer is not 'allowed' unless 0.999... has a finite end as:

1/0.999=1.001001001...
1/0.9999=1.000100010001...

Your answer is "not allowed" because it is demonstrably false. The calculation 1/0.999... ends up with a number with only one '1' in it; namely, 1.

We are only 'allowed' to repeat a finite sequence.

Agreed, but there is a finite repeating "sequence" in 0.999... it's the number '9' repeating over and over. With 1/0.999... the answer (1) has repeating 0's (1.000...), like most numbers do.

The rules change whenever infinity is involved.

Infinity isn't involved here though.

There would be an infinite number of zeros before each 1 which means the first 1 would never be reached.

NO! This is such an easy concept to grasp! You cannot have an infinite number of zeros "before" a 1...or ANY number. An infinitely long sequence of numbers by definition cannot have anything following it. The concept of 1.000...1 is completely invalid in mathematics; it is like trying to draw a square circle.

Again, it is easier to accept 0.999... as 1 than to redefine our mathematics involving infinities. A WHOLE lot easier.

There is no need to just "accept" 0.999... as 1, as long as you understand the mathematics behind infinities, which you clearly don't. There are various rigorous proofs of the concepts and calculations involving infinitely long numbers, and involving the concept of infinity itself. If you don't want to learn, that's up to you, but the fact is that these proofs do exist, and they are now well accepted and taught in mathematics.

This might help you out a bit: http://en.wikipedia.org/wiki/0.999...#Sk..._education