Dense math can often be complex to decipher. Sometimes it feels like reading an esoteric codebase to me! 1) Yes in this case 0 is not included in N. I’ve seen

Dense math can often be complex to decipher. Sometimes it feels like reading an esoteric codebase to me! 1) Yes in this case 0 is not included in N. I’ve seen N defined both ways depending on the context, so it can be confusing when it’s not given explicitly. 2) By definition, a series sum is based on the limit of partial prefix sums. E.g 1/a_1, 1/a_1+1/a_2, ... It is an interesting question mathematically, if the sum stays the same when you arbitrarily rearrange the terms of the series. In general the answer is no (see Riemann rearrangement theorem), but as this series is only made up of positive reals, it can be rearranged arbitrarily without change in how it converges (or doesn’t). To the second part of your question, take any geometric series, i.e. A = {1, r, r^2, ...}, then it will converge. There are other classes of series that will converge in this case, and the conjecture is basically asking to characterize sets with diverging series as needing to be “large and dense” in a certain sense.