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This question is related to notation of infinite product.

We know that, $$ \prod_{i=1}^{\infty}x_{i}=x_{1}x_{2}x_{3}\cdots $$

How do I denote $$ \cdots x_{3}x_{2}x_{1} ? $$

One approach could be $$ \prod_{i=\infty}^{1}x_{i}=\cdots x_{3}x_{2}x_{1} $$

I need to use this expression in a bigger expression so I need a good notation for this. Thank you in advance for your help.

  • 0
    What about simply $\,\,...x_3x_2x_1\,\,$?2012-05-24
  • 0
    What is the difference between the two products?2012-05-24
  • 0
    As I said there a big expression in which this sits. It is confusing and looks awkward. @ Michael Greinecker If matrices are involved you can tell the difference.2012-05-24
  • 5
    Presumably, the OP is regarding non-communicative multiplication.2012-05-24
  • 4
    I think the important question is "What do you mean by $\cdots x_3 x_2 x_1$?"2012-05-24
  • 0
    I have infinite matrices which have to be multiplied.2012-05-24
  • 1
    I would interpret the "backwards product" as the limit of $x_n x_{n-1} \cdots x_1$ as $n \to \infty$, so for commutative multiplication this is the same as the usual "forward product".2012-05-24

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