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# What do you get when you multiply all the real numbers? (kind of a trick question)

Question #61171. Asked by ogicu8abruok. (Dec 22 05 3:38 PM)

bojjie

Zero

 Dec 22 05, 5:18 PM
TabbyTom

Zero is a real number, so the product of all the real numbers is zero.

 Dec 22 05, 5:18 PM
ogicu8abruok

Ahh, but, if anyone out there is versed in the various forms of indeterminate limits would see why "zero" is not the answer, because this is a limit of type 0 times infinity. You could also think of pairing each number n with another real number, specifically 1/n, except zero, but then you have 1*0, so I'm looking for a mathematician who really knows his stuff to tell me what it really is.

 Dec 22 05, 6:37 PM
gmackematix

Given that the reals are not countable, I would dispute whether such a product has any meaning.

 Dec 22 05, 7:49 PM
peasypod

 Dec 22 05, 9:49 PM
ogicu8abruok

So, are you saying that a more interesting question would be what is the product of all the integers?

 Dec 25 05, 9:55 AM
peasypod

I'm saying to put the Rule of l'Hopital into action...

 Dec 25 05, 4:04 PM
ogicu8abruok

I was responding to gmackematix. And I wouldn't use l'Hopital's rule, because I don't even know if it's correct to conceive of it as a limit. Though that was clever.

 Dec 25 05, 9:35 PM
kevinom

if you are multiplying and not performing integration l'hopitals rule would not apply

 Jan 06 06, 7:15 AM

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