
Number Theory Number Theory Math Forum 
 LinkBack  Thread Tools  Display Modes 
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: 528 Thanks: 42 
No, because the set of hereditarily finite sets is countable.

April 3rd, 2019, 10:48 AM  #4  
Senior Member Joined: Aug 2012 Posts: 2,321 Thanks: 714  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.  

Tags 
combinations, countable set, elements, finite, infinite, sequences, set, uncountable set 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Finite and Infinite Sets  Luiz  Real Analysis  4  April 8th, 2015 05:56 AM 
Finite groups and functions on their elements  mojojojo  Abstract Algebra  1  March 17th, 2014 01:17 PM 
finite or infinite?  mathdigger  Number Theory  5  September 3rd, 2010 09:37 PM 
Construct finite field with q Elements (10^9<q<10^10)  Granit_niti  Abstract Algebra  6  February 8th, 2008 12:19 PM 
Sequences with a finite number of primes  Infinity  Number Theory  11  November 16th, 2007 04:50 AM 