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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?

JJJ
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  • There is none. How would one define it in a consistent manner? – Rushabh Mehta Mar 25 '19 at 18:18
  • 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 –  Mar 25 '19 at 18:27
  • 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. – Rushabh Mehta Mar 25 '19 at 18:29
  • Integration of the log? – David G. Stork Mar 25 '19 at 19:18
  • That seems to be wonderful!! –  Mar 25 '19 at 20:11
  • @DavidG.Stork excellent solution –  Mar 25 '19 at 20:11
  • I edited your question to remove your solution. If you really insist on putting the answer here, please use the answer box. If you want to indicate your question has been answered, please accept whatever answer (possibly your own) that you deem best. That way, others and the system will see your problem has been solved. – JJJ Mar 26 '19 at 14:43

1 Answers1

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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.

David G. Stork
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