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Thread: definitions

  1. #1 definitions 
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    Does this paragraph correct?!
    "sum symbolize by number of symbols, sigma, integral.
    While sigma - sum of numbers,
    and integral - sum of differences"
    I need exacter explantion than this of that terms - anyway, I am stuck"


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  3. #2 Re: definitions 
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    Quote Originally Posted by Shaharhada
    Does this paragraph correct?!
    "sum symbolize by number of symbols, sigma, integral.
    While sigma - sum of numbers,
    and integral - sum of differences"
    I need exacter explantion than this of that terms - anyway, I am stuck"
    Your question looks garbled. Could you clarify?


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  4. #3  
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    Does sigma symbolize sum of number?
    Does Integral symbolize sum of differences?
    what sum they are presented?
    Can I say that "all the integral are sum of differences" or not?
    I need exact definitions...
    Please explain it to me...
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  5. #4  
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    Sigma symbolizes sum of numbers.

    The definition of integral is given as part of a course in calculus. It does not symbolize a sum of differences. I cannot give you an exact definition unless I know what your mathematics background is. You need to be familiar with analytic geometry at least.
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  6. #5 Re: definitions 
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    Quote Originally Posted by Shaharhada
    Does this paragraph correct?!
    "sum symbolize by number of symbols, sigma, integral.
    While sigma - sum of numbers,
    and integral - sum of differences"
    I need exacter explantion than this of that terms - anyway, I am stuck"
    1. is a notation that is generally used to indicate a sum of some sort. The precise meaning depends on the details.

    2. The integral is really not notation, but rather a concept. There are several different fundamental definitions for the Riemann integral -- mesh integral, refinement integral, etc -- but in the end they are equivalent, There are also more general types of integrals -- Steiltjes, Lebesgue, Lebesque-Steltjes. The Labesgue integral agrees with the Riemann integral for functions that are Riemann-integrable and exists for some functions that are not Riemann integrable.

    In each of these cases the integral is not a "sum of differences" but rather a limit in the proper sense of summatins that are intuitively equal to areas of relative simple objects, rectangles in the case of the Riemann integral. The subtlety in the various definitions of the integral lies in the limiting process, and a rigorous description would be somewhat long and involved. The basic idea is that one can approximate the "area under the curve" for a suitable class of functions via the areas of an increasing refined approximation by rectangles.

    If you are "stuck" then you need to explain your particular problem in considerably greater detail. The nature of your difficulty is not at all clear.

    You might want to consult a good book on real analysis and the theory of integration. Rudin's Principles of Mathematical Analysis might be a good place to start.
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  7. #6  
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    Σ is the standard symbol for sum, not σ.
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  8. #7  
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    Nitpicking doesn't help your case.
    Wise men speak because they have something to say; Fools, because they have to say something.
    -Plato

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  9. #8 It is just an advice. 
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    I want to advice some idea.
    Please understand me coz I am an english user as second language.

    Firstly I want to show my level.
    I am just a begineer in mathematics.
    Why am I learning Math?
    I am a civil engineering student so I need some math formulae to understand.
    I think all of you above this topic are so active in math.
    I request a topic to call all kind of learners to their upper level.

    It is like ' Teaching Center In math " so on.

    Thanyawzinmin
    In the palace of Thanyawzin.
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