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 Jul12 comment Differentiating $y=x^{2}$ The prevalence of this 'proof by abuse of notation' nonsense has always been baffling to me. How can a mathematician justify dropping all rigor in favor of some logically inconsistent handwaving? May30 comment My son's Sum of Some is beautiful! But what is the proof or explanation? @anaximander: Of course if it were a 6th degree polynomial that would make perfect sense in the 6th grade. May14 comment Why is a full turn of the circle 360°? Why not any other number? Of course that should be 1/2, not 1/4. May14 comment Why is a full turn of the circle 360°? Why not any other number? @Zenon: Personally I think $A = \pi r^2$, $C = 2\pi r$ is nicer than $A = \frac{1}{4} \tau r^2$, $C = \tau r$, if only because it avoids the fraction. Feb13 awarded Teacher Feb13 answered Fractions in binary? Oct4 awarded Commentator Oct4 comment What's the probability that Abe will win the dice game? @Bobson: For a d3, wouldn't you normally take a d6 and map 1-2 to 1, 3-4 to 2, and 5-6 to 3? Oct1 comment using numbers 1 to 9 only once to equal 1 million I must have missed the step where base-2 '1000000' equals one million. Sep21 comment What is $dx$ in integration? This is a good explanation of the origin of the notation, but it doesn't quite explain why we bother to write it down. A big part of what the dx notation does is telling you the variable you're integrating over, and as a bonus parenthesizing the integrand. (The latter is probably why the teacher made the 'full stop' remark.) Jan21 comment Given a die, what is the probability that the second roll of a die will be less than the first roll? @Pureferret: Yeah, I agree he could have explained it better. Jan21 comment Given a die, what is the probability that the second roll of a die will be less than the first roll? @Pureferret: Considering that 1/6th of the possible rolls have A = B, 5/6th of the possible rolls have either A > B or A < B. Because of symmetry, half of that 5/6th will be A > B rolls, and the other half will be A < B rolls. Therefore the probability for an A > B roll is (5/6)/2 = 5/12. Does that help? Look at wvnl's answer for a formulaic approach to this reasoning. Dec24 comment What do you call numbers such as 100, 200, 500, 1000, 10000, 50000 as opposed to 370, 14, 4500, 59000 @David: I was talking about the OP there Dec23 comment What do you call numbers such as 100, 200, 500, 1000, 10000, 50000 as opposed to 370, 14, 4500, 59000 @David: And elsewhere tips are different. It's useless to discuss tips without specifying the cultural situation, so let's not get into that on a question not related to the subject. Nov1 comment How to sum this series for $\pi/2$ directly? @Srivatsan: Yes, of course. Just making a reference to youtube.com/watch?v=OQSNhk5ICTI Nov1 comment How to sum this series for $\pi/2$ directly? @ZevChonoles: Double factorial? What does it mean?! ;) Oct23 comment How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$? l'Hôpital's rule is easiest: $\lim\limits_{x\to0}\sin x = 0$ and $\lim\limits_{x\to0}x = 0$, so $\lim\limits_{x\to 0}\frac{\sin x}x = \lim\limits_{x\to 0}\frac{\cos x}1 = 1$ Oct17 awarded Supporter