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April 17th, 2019, 05:46 AM  #1 
Newbie Joined: Mar 2019 From: Belarus Posts: 10 Thanks: 0  Can an infinite sequence be missing one of such sequences?
Can an infinite sequence of finite sequences of combinations of a finite number of elements be missing one of such finite sequences? (If the rules do not prohibit such a finite sequence.) Last edited by Germann; April 17th, 2019 at 05:52 AM. 
April 17th, 2019, 06:32 AM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 
Looking at your past posts and this one (which is similar), I wonder what your purpose is... 
April 17th, 2019, 06:38 AM  #3 
Newbie Joined: Mar 2019 From: Belarus Posts: 10 Thanks: 0  
April 17th, 2019, 06:38 AM  #4 
Senior Member Joined: Oct 2009 Posts: 806 Thanks: 306  Yes, sure, such a finite sequence might be missing from the infinite sequence.

April 17th, 2019, 07:00 AM  #5  
Newbie Joined: Mar 2019 From: Belarus Posts: 10 Thanks: 0  Quote:
Why, then, the specific text of the novel will necessarily be printed, in the infinite monkey theorem? The text of the novel is the final sequence of a finite number of elements. The monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type any given text, such as the complete works of William Shakespeare. Last edited by Germann; April 17th, 2019 at 07:13 AM.  
April 17th, 2019, 07:56 AM  #6  
Senior Member Joined: Jun 2014 From: USA Posts: 528 Thanks: 43  Quote:
Lets add some clarity and say the monkey only draws natural numbers out of a hat randomly without replacement. Then the monkey may end up drawing all the naturals, just the evens, only the primes, etc. What are the odds that the monkey will draw all the naturals? What are the odds the monkey gets only the evens? These odds are undefined. It’s similar to asking whether a randomly selected real number is “normal” (see wiki or something) and trying to calculate the Lebesque Measure of the set of normal real numbers contained in [0,1] (the measure is 1). Last edited by AplanisTophet; April 17th, 2019 at 08:00 AM.  
April 17th, 2019, 09:12 AM  #7  
Senior Member Joined: Oct 2009 Posts: 806 Thanks: 306  Quote:
First of all, the infinite monkey theorem has some constraints. It won't always generate Shakespeare. Furthermore, the probabiliy it generates Shakespeare is 1, but this doesn't mean it HAS to generate Shakespeare! Of course, if you describe more in detail what the element of your infinite list look like, then the answer to your OP might be different. But if you put in no constraints and just specify "infinite list" and nothing more, the answer is no.  
April 17th, 2019, 09:26 AM  #8 
Newbie Joined: Mar 2019 From: Belarus Posts: 10 Thanks: 0  

Tags 
finite number of elements, infinite, missing, sequence, sequences 
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