What do you get when you multiply all the real numbers? (kind of a trick question)
Question #61171. Asked by ogicu8abruok.
bojjie
Answer has 1 vote
bojjie 19 year member
22 replies
Answer has 1 vote.
Zero
Dec 22 2005, 5:18 PM
TabbyTom
Answer has 2 votes
TabbyTom 23 year member
1233 replies
Answer has 2 votes.
Zero is a real number, so the product of all the real numbers is zero.
Dec 22 2005, 5:18 PM
ogicu8abruok
Answer has 2 votes
ogicu8abruok 20 year member
36 replies
Answer has 2 votes.
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 2005, 6:37 PM
gmackematix
Answer has 2 votes
gmackematix 21 year member
3194 replies
Answer has 2 votes.
Given that the reals are not countable, I would dispute whether such a product has any meaning.
Dec 22 2005, 7:49 PM
peasypod
Answer has 2 votes
peasypod 21 year member
3273 replies
Answer has 2 votes.
Indeterminatly thinking about this would lead one to the l'Hopital, yes?
Dec 22 2005, 9:49 PM
ogicu8abruok
Answer has 2 votes
ogicu8abruok 20 year member
36 replies
Answer has 2 votes.
So, are you saying that a more interesting question would be what is the product of all the integers?
Dec 25 2005, 9:55 AM
peasypod
Answer has 2 votes
peasypod 21 year member
3273 replies
Answer has 2 votes.
I'm saying to put the Rule of l'Hopital into action...
Dec 25 2005, 4:04 PM
ogicu8abruok
Answer has 2 votes
ogicu8abruok 20 year member
36 replies
Answer has 2 votes.
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 2005, 9:35 PM
kevinom
Answer has 2 votes
kevinom 19 year member
15 replies
Answer has 2 votes.
if you are multiplying and not performing integration l'hopitals rule would not apply
