03-10-2009, 01:18 PM
Zeno's dichotomy paradox doesn't even say that, it says you can't even begin to start towards the object. I guess you could kind of say that, but the mathematical definition of of real numbers is:
A cauchy sequences of rational numbers whose limit is X, where X is the real number in question, thus all real numbers are in fact limits of a sequence of rational numbers, which is why .9999... = 1.
A cauchy sequence is a sequence whose numbers become arbitrairly close to each other as the sequence progresses. Otherwise no matter what distance from 1 you want me to get .9999... to 1, I can always make it closer than that.
A cauchy sequences of rational numbers whose limit is X, where X is the real number in question, thus all real numbers are in fact limits of a sequence of rational numbers, which is why .9999... = 1.
A cauchy sequence is a sequence whose numbers become arbitrairly close to each other as the sequence progresses. Otherwise no matter what distance from 1 you want me to get .9999... to 1, I can always make it closer than that.
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