My Math Forum An infinite set of finite sequences of combinations of a finite set of elements

 Number Theory Number Theory Math Forum

 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? Thanks from Germann
 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. Thanks from Germann
April 3rd, 2019, 10:48 AM   #4
Senior Member

Joined: Aug 2012

Posts: 2,414
Thanks: 755

Quote:
 Originally Posted by Germann An infinite set of finite sequences of combinations of a finite set of elements is an infinite uncountable set?
Say the finite set of elements has cardinality $n$.

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.

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Luiz Real Analysis 4 April 8th, 2015 05:56 AM mojojojo Abstract Algebra 1 March 17th, 2014 01:17 PM mathdigger Number Theory 5 September 3rd, 2010 09:37 PM Granit_niti Abstract Algebra 6 February 8th, 2008 12:19 PM Infinity Number Theory 11 November 16th, 2007 04:50 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top