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We know that summation is for discrete values, and integration is the generalization of summation so that it can be extended to continuous values.

We also have product for discrete value, what is its continuous counter part?


marked as duplicate by J. M. is a poor mathematician, Cesareo, clathratus, Theo Bendit, Eevee Trainer Mar 27 at 4:21

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  • $\begingroup$ There is none. How would one define it in a consistent manner? $\endgroup$ – Don Thousand Mar 25 at 18:18
  • $\begingroup$ I am not sure, that is why I ended up asking the question. As multiplication is commutative, shouldn't we be able to generalize it $\endgroup$ – VARUN.N RAO Mar 25 at 18:27
  • $\begingroup$ Not really. Unless all but a finite number of values are 1, there is no way to define it properly. The linearity of addition makes it possible to define something like integration. $\endgroup$ – Don Thousand Mar 25 at 18:29
  • $\begingroup$ Integration of the log? $\endgroup$ – David G. Stork Mar 25 at 19:18
  • $\begingroup$ That seems to be wonderful!! $\endgroup$ – VARUN.N RAO Mar 25 at 20:11

Try: Integration of the logarithm.

Adding logarithms corresponds to multiplication.

Integration corresponds to summation.

So in the unusual question of putting together lots of multiplications, perhaps one approach is integrating logarithms.

But honestly, the question is a bit weird and poorly defined. I'm not sure it has a bona fide mathematical answer.

  • $\begingroup$ Can you elaborate more, please? As it stands this makes no sense to me (I'm probably missing something, of course). $\endgroup$ – YiFan Mar 26 at 6:06
  • $\begingroup$ David, do you mind clarifying? Because as far as I know, what @YiFan wants is likely the product integral - en.wikipedia.org/wiki/Product_integral $\endgroup$ – Eevee Trainer Mar 27 at 4:20
  • 1
    $\begingroup$ @EeveeTrainer Oh, thanks, but I wasn't thinking about that (I'm not the OP, btw). I'm just a passer-by cannot make sense of this answer. $\endgroup$ – YiFan Mar 27 at 5:46
  • $\begingroup$ Oops, my bad lol. $\endgroup$ – Eevee Trainer Mar 27 at 5:57

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