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 Dec11 revised Good books and lecture notes about category theory. Replace dead link Dec10 awarded Excavator Sep24 awarded Autobiographer Aug31 awarded Yearling Jun10 comment 'Obvious' theorems that are actually false @AnonymousPi $i = \exp\left(\frac{(4n + 1) \pi i}{2}\right)$ where $n \in {\Bbb N}$. Hence $i^i = \exp\left(\frac{-(4n + 1) \pi}{2}\right)$. Apr16 awarded Nice Answer Oct9 awarded Critic Sep27 revised Good books and lecture notes about category theory. fixed link (old link 404s) Aug31 awarded Yearling Jun11 awarded Nice Question May6 comment Prove $a+b+c+d$ is composite Note this does not work if you include 0 in the natural numbers. (Obvious counterexample: a = 0, b=3, c=0, d=4, so ab = cd = 0, but a+b+c+d=7 which is prime). Feb11 answered 2013th derivative of a trigonometric function Jan11 revised How to make two vectors orthogonal? added 227 characters in body Jan11 revised How to make two vectors orthogonal? Very sloppy bad math on my part. Jan11 revised How to make two vectors orthogonal? added 112 characters in body Jan11 answered How to make two vectors orthogonal? Jan11 comment How to make two vectors orthogonal? It's not Gramm-Schmidt. It's Gram-Schmidt (assuming you want to take a set of vectors that spans some space and create a new set of orthogonal vectors - typically also normalized - that spans the same space). Jan10 comment How to solve this calculus problem? @MaoYiyi - There an infinite number of potential functions $f(x)$ that satisfy the given property (e.g., if you assume a form of Ax^4 + Bx^3 + Cx^2 + Dx + E; then A=-134/2475, B = 3622/2475, C=-31924/2475, D=106937/2475, E= -7369/165; or you could assume Ax^10+Bx^8+Cx^6+Dx^4+Ex^2 and get a totally different answer that meets the criteria). E.g., you can give a rough estimate of f'(2.5) based on f(2), f(3) -- even if its more of an average value of f'(x) between 2 and 3. Jan10 comment How to solve this calculus problem? @proximal - I was trying to not suggest evaluate the limit, but to see f'(x) = lim h->0 (f(x+h) - f(x-h))/(2h) we can approximate f'(x) ~ (f(x+h) - f(x-h))/(2h) at several points, exactly as you said. Just was trying to leave it as "hints". Jan10 answered How to solve this calculus problem?