Roach412 wrote:....they will never be the same, as their value can always be adjusted by repeating the number again...and again...and again... fractals are similar example.

0.9... could be: 0.9999999999999999999999999999999

0.9... could be: 0.999999999999999999999999999999

they can be any variation of these, more 9's fewer 9's...doesn't matter. until you say "there! that's how many 9's there are", you simply do not have a real number from which to do equations with - it's an undefined limit.

Can't say I agree with that. 0.9... can't be 0.9999... or 0.99.... It is always 0.999... There are no more or less 9's at the end of any repeating string of 9's. Like I mentioned it isn't a "process". You are thinking of it as a repeating process or sequence when it should be thought of as a single number. Granted, not a solid number with a defined end, but it is still a value in "concept". A representation of something in a way.

Roach412 wrote:if you do not make a point at which the number ends, then yes, it really does not end - ever...over any amount of time space or anything. it quite literally is a race to infinity.

Can't really think of it in terms of a race, but if you do, then since they are the same they have to start at the same time. Neither is ahead or behind the other.

You can't say that one 0.999... might be different than another 0.999... by saying that one might have fewer or more 9's. You would then be assuming that one "started" sooner when numbers don't start at all to begin with. They are just numbers sitting there not going any direction in time or space. 0.999... can only be one thing, and it is the same as any other 0.999...