Quote:
Originally posted by klaucke
That's the thing-- .99999.... and 1 are not distinct, they are the same #. Between any two real numbers, there are actually an infinite number of other rational numbers (and reals too).
I typed the proof out in Mathematica so it'd be easier to see:
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That's not correct. The sum of a convergent infinite series is just the
limit of the series' partial sums as n tends to infinity. So you are only showing that the limit is equal to 1 which is completely different than showing that 0.9999... with an infinite number of 9's is equal to the number 1. You are basically just saying that the limit of X as X tends to 1 is 1.