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Question about inequality

  1. Dec 23, 2011 #1
    I posted the paragraph with the inequality where I am confused...

    I also added a portion i highlighted in red
     

    Attached Files:

  2. jcsd
  3. Dec 26, 2011 #2

    Curious3141

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    Homework Helper

    The text in the image is not very clear. One of the 'I's appears to have a line on the bottom, the other has the line on top.

    Regardless, the portion in the red box looks nonsensical. Everything before that makes sense.

    Let the s integral be represented by S, and the t integral be represented by T. Let's call the first I with the bar on the bottom A and the second I with the bar on top B.

    So the inequalities are:

    [itex]S \leq A \leq T[/itex] ---(1)

    and [itex]S \leq B \leq T[/itex] ---(2)

    Take (-1) times inequality 1. Remember to reverse all the signs:

    [itex]-S \geq -A \geq -T[/itex]

    Reverse the order of the terms (just write it backward):

    [itex]-T \leq -A \leq -S[/itex] ---(3)

    Add (3) to (2):

    [itex]S-T \leq B-A \leq T-S[/itex]

    and the latter half of that is what's given in the attachment (before the red box).

    What's in the red box looks wrong as I said - was that in the original?
     
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