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  1. G

    Compact sets and homeomorphisms

    I'm sorry, I didn't realize my question was ambiguous. But if there are no significant differences between metric and topological spaces, then your understanding is correct. Thank you for your answers. I'll try to be more specific in the future.
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    Compact sets and homeomorphisms

    Well, I'm out of my league here. I'm only in my first undergrad year and I haven't taken any topology yet (although I have Munkres' book and intend to put it to good use in the summer), so I'll have to study some before a proof or counterexample along those lines will make sense to me. This...
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    Compact sets and homeomorphisms

    Does the open mapping argument work because of the reasons I posted above?
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    Solving a Trigonometric Equation

    Does that equation have any real solutions? Or even complex ones? We know that for all x that |cos x| <= 1, and therefore |cos^n x| <= 1. So based on that we get cos x + cos^2 x + cos^4 x <= 1 + 1 + 1 = 3 < 4 so we must conclude that the original equation has no solutions.
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    Compact sets and homeomorphisms

    By the way, I first tried arguing that since f sends compact sets into compact sets, f also sends closed sets into closed ones. This doesn't hold because it says nothing about a closed set which isn't totally bounded and all bets are off on that one. Unless are no closed sets which aren't...
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    Compact sets and homeomorphisms

    Hmm... that's strange. I thought I managed to prove this earlier. Here's how: Let (M,d) and (N,r) be metric spaces, and f:M -> N a one-to-one and onto function. Assume that for every subset K of M holds K compact in M <=> f(K) compact in N Let's show that f is continuous. Take a...
  7. G

    Compact sets and homeomorphisms

    Hi there. I'm taking a course in analysis and I was thinking about the relation between compact sets and homeomorphism. We know that if f is an onto and one-to-one homeomorphism then it follows that for every subset K: K is compact in M <=> f(K) is compact in N Now, does this go the...
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    Elementary math that professors cant solve

    There's another fun variation on this theme where you line up all the numbers from one to nine in threes and are supposed to make them add up to six by adding only plus, minus, division, multiplication, root and power signs (whole powers and roots, no logs!). You can also use ( and ) (forgot...
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    Graphic calculators

    I see. I think I'll ask around at the university if there's any need for one of those, but do you have any reccomendations anyway?
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    Graphic calculators

    I'm starting university to learn mathematics and I'm looking for a good graphical calculator, what are good value-for-money models that would be useful for some time to come? Thanks, Gunnar.
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    Sinx and i

    I'm sorry, I'm from Iceland and math is tought in icelandic, so I don't know all the english names for functions. I'll look over what NateG posted tomorrow (kind of late here at GMT), since I've run into trouble deriving it myself the least I can do is learn how to do it properly. Thanks guys.
  12. G

    Sinx and i

    L = \int_{a}^{b}\sqrt(1 + (f'(x))^2)dx Anyway, thanks guys. Too bad that doesn't apply, seems the damn teacher was right. :smile:
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    Sinx and i

    Isn't that the definition of the sinh function? I always thought sin was defined as a/c in a triangle with one 90° corner.
  14. G

    Sinx and i

    Quick question. sin(-x) = -sin(x) this can be seen as this example: sin(i^2x) = i^2sin(x) Does this then apply? sin(ix) = isin(x) ? I'm trying to derive a formula for the length of a simple parabola. Unfortunetly in my calculations I end up with Arcsin(i2x) along the way and it...
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    2 fundmental ways of cryptography asymeteric and symeteric

    Cryptography is a complex field, you can't really sum up the methods of it in one equation (At least I can't), but there's an excellent book available by Simon Singh that's called "The Code Book" that tells you how cryptography was invented, how it was developed, how the modern cryptography...
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    Solving 3rd and 4th level equations

    I think one of my books mentioned a way of solving third level equations (ax^3 + bx^2 + cx + d) and fourth level equations (Same as before, add nx^4) much the same way as you do with second level equations ((-B +- Sqrt(B^2 - 4AC))/2A). I have two questions, do you guys know the formulas for...
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