
You do not understand what Hardy is saying. Here's the definition of a convergence of a sequence as if and only if Now, if we apply this definition to the sequence of partial sums Sn, to say that {Sn} converges to a means that for any positive real number epsilon we can find a positive integer N such that n > N implies that Sn' is within

Again, you are not correct. A series diverges if its sequence of partial sums does not have a limit. Take, for instance, the harmonic series Precisely because this series is unbounded, it is perfectly valid to say

This isn't quite true. An infinite divergent series is not a single number.


I agree with what Chomsky has to say about, "Support our troops": "[...] the point of public relations slogans like "Support Our Troops" is that they don't mean anything [...] that's the whole point of good propaganda. You want to create a slogan that nobody is going to be against and I suppose everybody will be for


Bloomj31 wrote one of the most neoconish posts I've ever seen here.

More explanations on the puzzle: http://en.wikipedia.org/wiki/Common_knowledge_(logic) http://plato.stanford.edu/entries/commonknowledge/#1.2

MMMark, I think you misunderstand my problem/solution. The outsider comes and says in public, "At least one of you has blue eyes." This is not the same as the outsider telling every person in private , "At least one of you has blue eyes." The latter would have no effect at all (unless n = 1) as intuition would suggest. Vive, What's

That's precisely why the answer is so counterintuitive. The outsider comes and doesn't tell the islanders anything new, but the process of telling the islanders this in public does something. The case for n = 3 is no harder. By the reasoning I just gave, each of the 3 blue eyes, sees other two and reasons that they must leave the 2nd dawn after