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Thread: product notation PI

  1. #1 product notation PI 
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    Let a product like
    a1 * a2 * a3 * a4
    be written like this :

    PI(k from 1 to 4) ak

    using the greek 'PI' symbol

    Does anyone know if reversing the limits makes the product equal to 1 ?
    (I suppose that for a sum, if the limits are in reverse order, sum = 0, no?)

    Meaning that
    PI(k from 4 to 1) = 1

    cheers


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  3. #2  
    Brassica oleracea Strange's Avatar
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    The product or sum will be the same either way as the operators are commutative: 2 x 5 = 5 x 2 so the order doesn't matter.

    Or, more generally (if I can get this right):


    Or have I misunderstood ?


    ei incumbit probatio qui dicit, non qui negat
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  4. #3  
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    Quote Originally Posted by Strange View Post
    The product or sum will be the same either way as the operators are commutative: 2 x 5 = 5 x 2 so the order doesn't matter.

    Or, more generally (if I can get this right):


    Or have I misunderstood ?
    No no you've understood, that was exactly my question.
    You'd think someone would decide to make it as i thought it was, cause it would be quite useful for simplifying the writing of fundamental mathematical proof in some cases.

    Just as it has been decided that 1 isn't a prime number, or that 0!=1

    Anyway thanks for quick reply !
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  5. #4  
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    By the way how did you get that symbol ? Is it on the forum or did you just copy it if off the web ?
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  6. #5  
    Brassica oleracea Strange's Avatar
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    Do you know LaTeX? If not, you should!

    You can embed LaTeX code between [tex] tags. The example above was created with: \prod_{k=0}^{n} a_k = \prod_{k=n}^{0} a_k

    If you are not familiar with LaTeX (or like me, just very rusty) there is a handy online interactive editor at: Online LaTeX Equation Editor - create, integrate and download
    ei incumbit probatio qui dicit, non qui negat
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  7. #6  
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    Awesome, cheers
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  8. #7  
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    Quote Originally Posted by Strange View Post
    The product or sum will be the same either way as the operators are commutative
    Hey, be careful! This is not true in general for the "multiplication operator".

    Like, matrix multiplication is not in general commutative, neither is the product of permutations.

    In fact, commutativity of the multiplication operator is only valid for a ring (of which a field, like is an example). But is a ring but not a field, but still admits of commutative multiplication.

    Sorry to be boring, but in mathematics it is always useful to specify the domain in which you are working.

    Poor old G! Has he nothing better to do with his life? (Don't answer.....)
    Strange likes this.
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