Non integer square roots and pi = irrational?

HallsofIvy

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.

matt grime

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

Charles Babbage.

Leonardo Sidis

Anyone who conducts an argument by appealing to authority is not using his intelligence; he is just using his memory.

-Leonardo da Vinci

HallsofIvy

Would you mind pointing out where, in this thread, there was an "appeal to authority"?

(as opposed to stating standard definitions.)