(November 3, 2011 at 9:02 am)edk141 Wrote:(November 3, 2011 at 12:18 am)IATIA Wrote: It is accepted because the definition of numbers requires a divisible space between each. Because there is no divisible space between 0.999... and 1, it is accepted as 1. The proofs, however, are all wrong. But we do not know what else to do with this number without shaking the foundations mathematics.
The proofs are correct. Any repeating decimal number is merely a representation of an exact rational number.
You cannot use infinities in algebra and a repeating decimal falls into the infinity category. In calculus infinities are calculated as limits. As in "approaching 1", but does not equal one. Infinities are strange and do not conform to our mathematics. A piece of infinity is still infinity. Two infinities are not twice as big as one infinity. One cannot calculate an infinite progression because that would take an infinite amount of time, but through calculus, we can calculate the limit. Like I said though, it is accepted as 1 because the definition of numbers states that between any two real numbers there is another real number. So technically, 0.999... is not even a real number. (then again, maybe 1 is the unreal number )
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-- Homer Simpson
God has no place within these walls, just as facts have no place within organized religion.
-- Superintendent Chalmers
Science is like a blabbermouth who ruins a movie by telling you how it ends. There are some things we don't want to know. Important things.
-- Ned Flanders
Once something's been approved by the government, it's no longer immoral.
-- The Rev Lovejoy