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April 3rd, 2019, 10:38 AM  #1 
Newbie Joined: Mar 2019 From: Belarus Posts: 10 Thanks: 0  An infinite set of finite sequences of combinations of a finite set of elements
An infinite set of finite sequences of combinations of a finite set of elements is an infinite uncountable set?

April 3rd, 2019, 10:42 AM  #2 
Senior Member Joined: Jun 2015 From: England Posts: 915 Thanks: 271 
How does the set get to be infinite if there are only a finite number of members available?

April 3rd, 2019, 10:46 AM  #3 
Senior Member Joined: Jun 2014 From: USA Posts: 623 Thanks: 52 
No, because the set of hereditarily finite sets is countable.

April 3rd, 2019, 10:48 AM  #4  
Senior Member Joined: Aug 2012 Posts: 2,414 Thanks: 755  Quote:
There are $n$ distinct sequences of length 1. There are $n^2$ sequences of length 2. In general there are $n^k$ distinct sequences of length $k$. The union of countably many finite sets is countable.  

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combinations, countable set, elements, finite, infinite, sequences, set, uncountable set 
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