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 Dec 6 comment Prove by induction that $5^n - 1$ is divisible by $4$. Nice, clear, clean... a good answer indeed! Sep 19 comment A function that creates a partition of values such that the sum is 1 Thank you!!! Do you know is this function has some special name (other than geometric series)? (I know I found it in a book some years ago, but I can't remember the name... or the book) Sep 19 comment A function that creates a partition of values such that the sum is 1 duh, right! Forgot to write that $k$ is a (deterministic) parameter of the function Sep 19 comment A function that creates a partition of values such that the sum is 1 $k$ is a real number in the interval $(0,1)$ Sep 19 comment A function that creates a partition of values such that the sum is 1 @Donkey_2009 No, I mean exactly the natural numbers... I'm editing the question to make it more clear Sep 17 comment How can one prove that $e<\pi$? Fast, simple, elegant... Love it! Aug 27 comment math fallacy problem: $-1= (-1)^3 = (-1)^{6/2} = \sqrt{(-1)^6}= 1$? I think that it should be noted that $\sqrt{a^2} = | a |$. So, when you calculate $\sqrt{(-1)^6}$ you are doing something like this: $\sqrt{(-1)^6}=((-1)^2)^\frac{3}{2}=\left(\sqrt{(-1)^2}\right)^3=(|-1|)^3=1$ Apr 10 comment How can I prove that $xy\leq x^2+y^2$? Quite an elegant hint! Oct 3 comment How do you find the center of a circle with a pencil and a book? This solution is far better than the accepted one, since it does not depends on perception ("put the corner of the book..." how do you know that you are really drawing a diameter?). +1 for this answer! Sep 21 comment What is $dx$ in integration? Quite a good explanation Sep 20 comment What are imaginary numbers? @CliveN. Man! This is one of the greatest, clearest, coolest and simplest answers I've ever seen for this question (and funniest, I had a lot of fun reading it). I will quote it every time I get the chance! +1 (If I could vote more than one time, I would) Aug 21 comment Which symbol should be used for an empty set? This is not a constructive question... It's just about "what symbol is better"... it's a matter of preference! Jun 20 comment Is it wrong to say $\sqrt{x} \times \sqrt{x} =\pm x,\forall x \in \mathbb{R}$? Notice that $\sqrt{x^2}=|x|$, so it can be said that $\sqrt{x^2}=\pm x$ Jun 17 comment Is it wrong to say $\sqrt{x} \times \sqrt{x} =\pm x,\forall x \in \mathbb{R}$? @Théophile ook... $x\geq0$ Jun 7 comment What is the chance to get a parking ticket in half an hour if the chance to get a ticket is 80% in 1 hour? @MarkAdler Thank you Mark... I will soon correct my answer to include this calculation for the value of $\lambda$. And yes, Math is beautiful! :-) Jun 5 comment What is the chance to get a parking ticket in half an hour if the chance to get a ticket is 80% in 1 hour? That said, I'm correcting my answer, because I calculated the probability of "being spotted" once per interval, which is not what we are looking for. The probability we're looking for is "what is the probability of 'being spotted' at least one time", which is 1 - Pr{"Not 'being spotted'"}. Jun 5 comment What is the chance to get a parking ticket in half an hour if the chance to get a ticket is 80% in 1 hour? With no further information, the expected value of the tickets per hour is 0.8 (is a Bernoulli experiment). I think the Poisson Process hypothesis holds because all you know is that you may "get caught" with a given probability in a unit of time. Of course you can't be caught more than once a day, but that doesn't implies that you can't be "spotted" n times a day.