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 September 6th, 2015, 03:58 AM #1 Senior Member   Joined: Sep 2015 From: 4th Dimension Posts: 146 Thanks: 13 Math Focus: Everything (a little bit) let's see who is the fastest Find the value of $\displaystyle 2!!!!!!!!!!!!!!!!!!............................... ...........................!!!!!!!!!!!! \text{(Upto infinity)}$ Last edited by skipjack; September 6th, 2015 at 05:26 AM.
 September 6th, 2015, 03:59 AM #2 Senior Member   Joined: Sep 2015 From: 4th Dimension Posts: 146 Thanks: 13 Math Focus: Everything (a little bit) Is it me???
 September 7th, 2015, 09:47 AM #3 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 I have no idea what you are talking about. How do measure the time taken to look at that and say "that number does not exist"? (No, your signature is not interesting.) Thanks from topsquark
September 7th, 2015, 08:53 PM   #4
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Quote:
 Originally Posted by Country Boy I have no idea what you are talking about. How do measure the time taken to look at that and say "that number does not exist"? (No, your signature is not interesting.)
The no. Does exist.

 September 7th, 2015, 10:52 PM #5 Math Team   Joined: Nov 2014 From: Australia Posts: 689 Thanks: 244 Well, $2! = 2$, so if we take factorials a finite number of times, we get $$2!!!!...! = 2.$$ However, I have no idea what would happen with an infinite number of factorials (or even if the concept is well defined). Thanks from Monox D. I-Fly
 September 8th, 2015, 09:04 AM #6 Senior Member   Joined: Sep 2015 From: 4th Dimension Posts: 146 Thanks: 13 Math Focus: Everything (a little bit) We can prove that it is true for every $n+1$ and hence it is valid upto $\infinity$
 September 9th, 2015, 12:27 AM #7 Math Team   Joined: Nov 2014 From: Australia Posts: 689 Thanks: 244 No. You can conclude that it is true for any positive finite number of factorials. The problem I have is that it is not clearly defined for an infinite number of factorials. One way to formally define it would be: Find $\displaystyle\lim_{n\to\infty}a_n,$ where $$a_1 = 2,\qquad\qquad a_{n + 1} = a_n!$$ Thanks from Yash Malik

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