Yes, they do have difficulty. People who say that people who have trouble believing 1=0.999... are idiots are themselves having difficulty. 1 and 0.999... are different kinds of mathematical objects, hence in some sense they are not equal.

0.999... is not a "decimal expansion" of some number, but rather it denotes a sequence of numbers: 0.999, 0.9999, 0.99999, ....

The fact that "the real numbers can be defined as equivalence classes of Cauchy sequences of rational numbers" is probably not obvious to most of the people who think 0.999...=1 is obvious, and they would probably be surprised at how deep this area of mathematics is. See P-adic_number.

Also, one should not just casually accept the ideas of infinite series and sequences, because counter-intuitive things DO happen with them. There is no such thing as an "infinite decimal expansion" or "adding up an infinite number of numbers" -- those are just analogies, which may or may not mislead you in a given situation.

Also, the paper was presented at an astrobiology conference. They are suggesting that an alien civilization is more likely to have built one of these than an actual Dyson sphere (because it seems possible with our own technology within the next 100 years, unlike a Dyson sphere), and they are wondering if we would be able to detect it using our current instruments and techniques. That's the focus of the paper, not the idea that we should actually begin building one.

I think their point is that it scales up very well. The sail material is relatively cheap, and the main cost would be deploying it and getting the power back to earth, so it probably makes sense to use a really, really big sail. The bigger you make it, the cheaper it will be (per GW), much more so than any existing sources of power. Of course, that assumes the power transmission can also be scaled up, and they haven't figured out that part yet.

No, I think it ends with Microsoft trying to sell pumpkins disguised as smartphones. It's a shorter story than the original.

To be honest, I think that's a fair price for so much music...IF the bulk of the money actually went to the artists (and recording engineers, and producers) who made that music, rather than to industry leeches.

Why doesn't Microsoft make EMET part of Windows Defender, and auto-update the settings for various applications/DLLs (like the way they update compatibility-mode settings for websites in IE8)? They could have prevented this exploit on day 1.

I recall one explanation put forth was bats getting sucked into jet engines, or something similar. But there are a lot more birds around than bats, so if that happened you'd expect to see other red rains where the cells do contain DNA (as birds' red blood cells do).