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 Nov27 comment Is the empty set the only possible set for $A$ such that $A=\{x|x\not\in A\}$? The most understandable answer. :-) Thanks. Aug9 comment How to test whether a set of four points can form a parallelogram We can save the calculation just by calculating the midpoint times 2 to avoid dividing by 2. Aug9 comment How to test whether a set of four points can form a parallelogram How about the case there are 3 points on a line? Aug9 comment How to test whether a set of four points can form a parallelogram But all of your three tests may be false even though the given 4 points can be vertices of a parallelogram. Aug9 comment How to test whether a set of four points can form a parallelogram If $P_1$ is the opposite of $P_3$ then the last two tests are false. So the first test might be either false or true. Aug9 comment How to test whether a set of four points can form a parallelogram I think we need 4 tests. Your answer needs one more test which is $\vec{P_1P_2}=\vec{P_3P_4}$. Aug9 comment How to test whether a set of four points can form a parallelogram Please explain why you compared just those vectors. Aug9 comment How to test whether a set of four points can form a parallelogram @augurar: The given points are randomly chosen from a set of some points. The order is not known. Jul4 comment Is my theorem correct? $f(x) \leq g(x)$ for $x\geq a$ iff $f'(x) \leq g'(x)$ for $x\geq a$ and $f(a)=g(a)$. what is the name of the well known corollary? Jul4 comment Is my theorem correct? $f(x) \leq g(x)$ for $x\geq a$ iff $f'(x) \leq g'(x)$ for $x\geq a$ and $f(a)=g(a)$. By assuming the right side is satisfied first and prove that the left is either correct or incorrect. Jul4 comment Is my theorem correct? $f(x) \leq g(x)$ for $x\geq a$ iff $f'(x) \leq g'(x)$ for $x\geq a$ and $f(a)=g(a)$. Could you prove in both directions? May7 comment What is the non-piecewise curve that resembles the following roller coaster track? @Neil: Any parameter is accepted. May7 comment What is the non-piecewise curve that resembles the following roller coaster track? @vonbrand: I don't want to use if-then-else construct in my code. :-) May7 comment What is the non-piecewise curve that resembles the following roller coaster track? I cannot show my effort to solve this problem. Is it necessary to show it? May7 comment Functions Question Commutative by accident. Mar11 comment How to prove that we cannot see more than 3 faces of an opaque solid cube simultaneously? +1. Makes sense! Mar11 comment How to prove that we cannot see more than 3 faces of an opaque solid cube simultaneously? But you can see 3 faces by focusing on one corner. Feb10 comment How to prove the number of images of two mirrors inclined at $A$ is $360/A -1$ +1 Short respons: I ask myself to prove it analytically. :-) I will give other comments later as I am teaching right now. :-) thanks. Jan21 comment How to find the closed solution for the following recursive vector equations? OK. I am waiting for other solutions if any. Jan21 comment How to find the closed solution for the following recursive vector equations? @heropup's solution in his comment seems to be much more better.