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## Non integer square roots and pi = irrational?

 Quote by Leonardo Sidis Actually, your previous post made this relate specifically to this thread. One cannot find the exact sum of an infinite series of numbers, only the finite number that it may approach. This is the reasoning behind the paradox; since one can always find a number smaller than another, an infinite amount of finite distances must be travelled to travel at all.
If that is the reasoning behind the paradox, it's no wonder you get a paradox! One certainly can find the exact sum of an infinite series of numbers. For example the sum 1+ 1/3+ 1/9+ 1/27+ ... is exactly 1.5. That is not a "finite number that it may approach". I'm not certain what you mean by "it" here. If you mean the sum, it is not approaching anything, it is 1.5. If you mean the sequence of partial sums (which is what many people mean when they talk about something like this), there is no "may" that sequence is approaching that number and so sum is, by definition, 1.5.

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 Quote by Leonardo Sidis Actually, your previous post made this relate specifically to this thread. One cannot find the exact sum of an infinite series of numbers, only the finite number that it may approach. This is the reasoning behind the paradox; since one can always find a number smaller than another, an infinite amount of finite distances must be travelled to travel at all.

I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question.

Charles Babbage.

 Quote by matt grime I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question. Charles Babbage.
Anyone who conducts an argument by appealing to authority is not using his intelligence; he is just using his memory.

-Leonardo da Vinci

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