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Math Help - Intro to Analysis

  1. #1
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    Intro to Analysis

    I just started this class and for some reason the material isn't clicking at all. I was wondering if anyone could give me some sort of hint on how to approach this problem. I would GREATLY appreciate it.

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  2. #2
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    Quote Originally Posted by haikuambulance View Post
    I just started this class and for some reason the material isn't clicking at all. I was wondering if anyone could give me some sort of hint on how to approach this problem. I would GREATLY appreciate it.

    I will do the first bit:

    x = qx + (1 - q) x < qx + (1 - q)y for x < y.

    y = qy + (1 - q) y > qx + (1 - q)y for x < y.

    Therefore x < qx + (1 - q)y < y for x < y.
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  3. #3
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    Here's how I would do it. Since x< y, y- x> 0. Since q< 1, subtracting q from each part, 0< 1-q. Since 0< q, -q< 0 and 1- q< 1. Setting p= 1- q, we also have 0< p< 1. multiplying each part by the positive number y- x, 0(y-x)< p(y-x)< 1(y-x) or 0< py- px< y- x. Adding x to each part, x< py- px+ x< y. -px+ x= (1- p)x= qx and py= (1-q)y so that is x< (1- q)y+ qx< y.

    (I first did that using "q" rather than "p" and arrived at x< qy+ (1-q)x< y which is true but not what is wanted. That when I switched to p= 1- q and did the same proof.)
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