Recent content by trap101

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    Functional relation and implicit functions

    This is more a conceptual question. So i am doing some self review of multi variate calculus and i am looking at functinal relations of the form F(x, y, z,...) = 0 In the book they talk about implicit differentiation. Now i fully understand how to do the mechanics of it, but i was trying to...
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    Topology or logic or other start point?

    The most my school offered when i took the courses was "concepts in abstract math" so there was no direct intro to proofs course, of course the school has now realized their mistake and created the course, but it is a first year course and i don't think i am eligible for it anymore considering i...
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    Topology or logic or other start point?

    So i just recently had to drop two math courses, topology, math logic, because my math maturity wasn't up to the level needed to excel in them. I intend on taking them again, but not without first more preparation which leads to my question. Which order would i benefit more from in preparing for...
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    Showing that a given function is continous over a certain topology

    Yes, but how do they get that singleton is my question. Is it that you look at each inverse image of each coordinate function individually and take the intersection of those , which produces the common point 0?
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    Showing that a given function is continous over a certain topology

    Consider the maps h: R^w (omega) ---> R^w (omega) , h (x1, x2, x3,...) = (x1,4x2, 9x3,...) g: (same dimension mapping) , g (t) = (t, t, t, t, t,...) Is h continuous whn given the product topology, box topology, uniform topology? For the life of me i am...
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    Proving B(r,x) is a Subset of S^c: Basic Topology Question

    Yea I just copied the code wrong for that, but no i was not aware of the triangle inequality in that form. I'm gping to go derive it now. Thanks. If I have an issue I will ask for assistence
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    Proving B(r,x) is a Subset of S^c: Basic Topology Question

    Ok using: $$\|y\|\geq\|x\|-\|y-x\|.$$ I was trying this before but didn't feel it would be valid. Now since ##r=\|x\|-\rho##, I can then say ## r + \rho = \|x\|## now can I say that: ##\|y\|\geq\|x\|-\|y-x\|\geq r + \rho = \|x\| - r## which wold reduce to ##\|y\|\geq\rho ##
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    Proving B(r,x) is a Subset of S^c: Basic Topology Question

    Sorry. S is B(\rho, 0) , that is the ball of radius \rho about the origin.
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    Proving B(r,x) is a Subset of S^c: Basic Topology Question

    I apologize my writing of the question is very messy. You are right on both counts. X is a vector in Rn, Sc is the complement of S, and S is a subset of Rn. Sorry for making it messy.
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    Proving B(r,x) is a Subset of S^c: Basic Topology Question

    Assume ##|X| > \rho## , let ##r = |X| - \rho## Now I am trying to show that ##B(r,x)\subseteq S^c## This should be a simple question, but I am struggling trying to find the right inequlity. Attempt: let ##y## be a point in ##B(r,x)##. I know that ##|x - y| < r##. I have to somehow show...
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    Showing a sequence converges to 0

    Got it. Thanks all for the help.
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    Showing a sequence converges to 0

    Ok so if I may summarize to make sure I got the thinking right. So at our inductive we assumed that 2^k/k! <= 4/k. decomposing 2^(k+1)/(k+1)! = (2^k/k!)(2/(k+1)) so this provides me with the hint that I multiply both sides of 2^k/k! <= 4/k by (2/(k+1)) now since by assumption we...
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    Showing a sequence converges to 0

    Ok so I thought I had it figured out, but apparently not. So moving along we've established that it suffices to show that (4/k)(2/(k+1)) <= 4/(k+1) and I will be done. So going with the hint from pasmith I found that if 2 <= K then this inequality will hold. But I feel I am still missing...
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    Showing a sequence converges to 0

    Bloody hell, that's what I was missing to do, I've been trying to polish up on these processes for the new year. So now there is no factorial which makes it a lot easier. Of course it would be induction again on this piece correct, but no factorial should make it more straight forward. If I have...
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    Showing a sequence converges to 0

    I tried that before and got (2^k/k!)(2/(k+1)) <= (4/k)(2/(k+1)) Now by inductive hypothesis I know already that (2^k/k!) <= (4/k), and just multiplying both sides of that doesn't change that, but I feel I still need to have 4/(k+1) to appear in the inequality somewhere.
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