0.99999~ = 1 ?

Thank you Rhain for so forcefully showing how 0.99999999999999999999999999999999999999999999999999999999999999999999999999999999... is the same as 1.0.I just might want to present a useful way to bring 0.999~ into mathematical discussion. Surely you are acquainted with the concept of open and closed intervals on the Real Number axis.you have seen such things as [0.0, 1.0] and (0.0, 1.0). the former means we INCLUDE 0 and 1 and the latter means we do not, but everything in between. we even have such things as [0.0, 1.0) or (0.0, 1.0] which will include 0 or 1 respectively.someone could argue that 0.999~ is a beautiful way to represent the upper limit of the open interval (0.0, 1.0).give me an epsilon and i can get a delta (etc.).another topic:
the Heine-Borel Theorem is one of the coolest things ever.

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- xongsmith, 5.7d

You are confusing 2 different things, the number itself, which is finite, and the way we would write it down, which is infinite (but for the shorthand symbol |, fortunately).

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- xongsmith, 5.7d

Jon objects: Again, don't confuse the ascii letter representation with the number itself.0.999| is a perfectly good equivalent of 1.0 or 1. It's just not as efficiently represented by our ascii character set.3.14159 is an approximation of pi and not identical to pi. We have no way of representing the series of digits continuing out ad-infinitum for pi.We might try pi = 4*arctan(+1.0) or 4*atan(1) in some computer languages which is 9 ascii characters.orln( -1)
----------- could be ln(-1)/i, which is only 8 characters.
ior arccos(-1) is another way.Some computer languages will even allow you to write "pi", only 2 characters, but inside the machine there is a value of the 3.14159 kind, with as many digits as their long double may hold. So it's really, again, not identical. And this is also true of those other constructs above, because ultimately the computer has a limited storage ability for calculating things like 4*atan(1).The notation we use to represent the number is never meant to be the same as the number itself.

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- xongsmith, 5.7d