Billy
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 Jul 30 awarded Yearling Jul 30 awarded Yearling Nov 13 awarded Enlightened Nov 13 awarded Nice Answer Nov 13 awarded Nice Answer Jul 30 awarded Yearling Jul 30 awarded Yearling May 16 awarded Nice Answer Jan 9 comment When two functions are equal, but not. @HexagonTiling: I'm not sure. In my mind, a 3-tuple is a very fixed and well-defined object. You may define it differently if you like, and indeed if you're working very strictly inside some logical system maybe your hand is forced here, but it is only when we collaborate that we make the implicit identification between our two definitions. Homeomorphic topological spaces are most definitely not identified except when we have decided that we only care about the topology - elliptic curves are a good example of this. Though perhaps that's important to point out in its own right. :) Jan 9 comment When two functions are equal, but not. @wim: There are many people (myself included) who do not consider the delta function to be a function. (Though perhaps you're right that it still needs mentioning, even if just to say that.) Jan 8 answered When two functions are equal, but not. Jan 8 comment Algebraic conjugates I like this answer - an honest answer to this question has to mention Galois theory somewhere, at least implicitly, in my opinion - but from the language used, I'm slightly concerned the thread starter might not have done much Galois theory. Nov 25 awarded Critic Nov 25 comment Are there other ways to calculate integrals or a way to keep all these formulas apart? @Simon: the obvious and easiest way to learn anything is to understand it - go and work out what integrals are, and the formulas should start to make sense! Sep 30 comment Vector Theory Question The parallelogram law is by far the most sensible way to do things intuitively, and that is formalised by the triangle inequality. But here's a brute force way. Rotate the whole system. This obviously won't change any lengths or angles or anything. Specifically, rotate it until the vector u becomes (3,0). Now v still has size 5, so can be anything of the form (5 cos x, 5 sin x) for some number x. Which one maximises || u + v ||? Sep 30 comment Sets and Relations I'm not sure what you're struggling on. Have you worked out whether any of the three properties hold? Two should be very easy, provided you understand the definitions. One might take a bit more thought. Sep 24 comment Chain rule and a square in the denominator @Jordan: you definitely didn't have that. All of your later working followed as if it was just $(r^2+1)$. In other news, don't forget that you have to divide by the square of the denominator to apply the quotient rule, which (on second reading) it doesn't look like you've done. Sep 24 answered Chain rule and a square in the denominator Sep 18 comment Point reflection over a line It might help to note that $a + ib = (dx + i\cdot dy)^2 / |dx + i\cdot dy|^2$, and indeed that the author of this code is making quite heavy use of complex numbers. Draw yourself a diagram and have a look at what x2 and y2 do. Sorry I don't have time to elaborate more... Sep 17 comment How to prove $\log n < n$? @Mark: No, this isn't what big O notation is about. Big O describes limiting behaviour (e.g. as two functions go to infinity), and says nothing about what they do elsewhere.