Can an infinite sequence be missing one of such sequences?

Mar 2019
10
0
Belarus
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:

Denis

Math Team
Oct 2011
14,592
1,026
Ottawa Ontario, Canada
Looking at your past posts and this one (which is similar),
I wonder what your purpose is...
 
Oct 2009
942
367
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.)
Yes, sure, such a finite sequence might be missing from the infinite sequence.
 
  • Like
Reactions: 1 person
Mar 2019
10
0
Belarus
Yes, sure, such a finite sequence might be missing from the infinite sequence.
If the rules do not prohibit such a finite sequence?

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:
Jun 2014
650
54
USA
If the rules do not prohibit such a finite sequence?

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.
It’s random so anything is possible. Consider the case where the monkey generates the same finite set over and over so as to only get one.

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:
  • Like
Reactions: 1 person
Oct 2009
942
367
If the rules do not prohibit such a finite sequence?

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.
Now you are asking a different question.
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.
 
  • Like
Reactions: 1 person