Greg L
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 Dec17 awarded Favorite Question Jul2 awarded Curious May19 awarded Yearling May3 awarded Necromancer Mar10 comment Why do statisticians like “$n-1$” instead of “$n$”? One non-technical explanation I've heard is that when your sample size n = 1, variance is undefined, which the division by zero cleverly ensures :) Feb3 comment Is it faster to count to the infinite going one by one or two by two? The speed at which you approach infinity by counting is always zero, no matter how fast you count, because the distance from where you are to infinity never changes. Nov28 awarded Notable Question Sep3 comment How do you define the “boundary” of a topological space? +1 for use of the word "irregardless". Aug23 comment Intuitive explanation for how could there be “more” irrational numbers than rational? What an excellent way to think about it. You can even show that the probability of "rolling" a rational number is zero under the requirement of an infinite number of digits! Jul15 comment How many numbers can I make with subseries of $\sum_{n=1}^{\infty} \frac{1}{2^n}$? @AndresCaicedo, thanks for the reference but your link is broken, is tufts.edu/~znitecki/Subsum%20Sets%20(v9).pdf the correct paper? Jul15 comment How many numbers can I make with subseries of $\sum_{n=1}^{\infty} \frac{1}{2^n}$? Oof, of course the interval is [0,1], I feel stupid :) Jul15 accepted How many numbers can I make with subseries of $\sum_{n=1}^{\infty} \frac{1}{2^n}$? Jul15 comment How many numbers can I make with subseries of $\sum_{n=1}^{\infty} \frac{1}{2^n}$? Thanks! I take it that this approach can also show that if we change 2 to any other natural number, we cannot find subseries that converge to arbitrary reals in the appropriate interval, because the numerator remains equal to 1 and so not every decimal expansion in the corresponding base can be recreated? Jul15 comment How many numbers can I make with subseries of $\sum_{n=1}^{\infty} \frac{1}{2^n}$? Every real number in [0.5,1] is of the form 0.XXX... where X is 0 or 1, and each digit corresponds to a term in this series? Jul15 asked How many numbers can I make with subseries of $\sum_{n=1}^{\infty} \frac{1}{2^n}$? May9 awarded Caucus Feb8 awarded Yearling Jan22 comment How to read letters such as $\mathbb A$, $\mathbb B$, etc., or $\mathfrak A$, $\mathfrak B$, etc.? That's an A? I always thought it was a U... Jan4 comment What's a proof that the angles of a triangle add up to 180°? @ Joe Zeng: Yes but when you "fold" the triangle you are just reflecting the top vertex of the triangle onto another line parallel to the base of the triangle (but that line just happens to be the base itself, i.e. a line is parallel to itself). The reflection preserves angles and the final geometric analysis is similar (just rotated 90 degrees). I'm not disagreeing with you per se, just pointing out how your "folding" technique is actually more rigorous than you give it credit for! Jan4 comment What's a proof that the angles of a triangle add up to 180°? This proof seems more or less identical to the one you present in your question.