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Math Help - Definition Of A Double Integral

  1. #1
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    Definition Of A Double Integral

    Hello,

    I am currently reading about the preliminary work used to define the double integral, and there is one thing my author states, whose meaning I am not certain I understand. Here is an excerpt:

    "The rectangles lying entirely within R form an inner partition whose norm || \Delta || is defined as the length of the longest diagonal of the n rectangles."

    Could someone possibly explain the meaning of this to me, especially the part about the longest diagonal?

    Thank you in advanced!
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  2. #2
    Member Ruun's Avatar
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    Re: Definition Of A Double Integral

    It means that the rectangles in the partition doesn't have to be all of the same size, so their diagonals will be different. When the limit ||\Delta|| \to 0 will be taken, to smaller rectangles will also tend to "zero"
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