November 15th, 2017, 05:22 AM  #1 
Newbie Joined: Nov 2017 From: Hooksett NH Posts: 1 Thanks: 0  Counting Functions
Hi: I'm trying to understand counting functions between two sets. For example, between two 3element sets, there are 3^3=27 functions. And there are 3!/0!=6 onetoone functions. What are the other 21 functions? Thayer 
November 15th, 2017, 05:30 AM  #2  
Senior Member Joined: May 2016 From: USA Posts: 1,310 Thanks: 551  Quote:
(1) a to x, b to x, c to x; and so on.  
November 16th, 2017, 04:11 AM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
With, as JeffM suggested, {a, b, c} as domain and {x, y, z} as range the 6 "onetoone" functions are a> x, b> y, c> z a> x, b> z, c> y a> y, b> x, c> z a> y, b> z, c> x a> z, b> x, c> y a> z, b> y, c> x The other 21 functions are, of course, those that are NOT "onetoone". That is, more than one of the members of the domain are mapped to the same member of the range. Of course since the domain and range have the same finite cardinality a function that is not "onetoone" cannot be "onto". One example is a> x, b> x, c> x. Another is a>x, b>y, c>y. 
November 17th, 2017, 07:13 AM  #4 
Senior Member Joined: Feb 2010 Posts: 706 Thanks: 140 
I think there are only 18 functions from {a,b,c} to {x,y,z}. The total of 27 would include things like: a > x, a > y, a > z which is a relation but not a function. 

Tags 
counting, functions 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
counting  jroff419  Probability and Statistics  9  May 5th, 2017 07:27 PM 
Fourier Series for Prime Counting Functions  SteveC  Number Theory  3  October 14th, 2016 02:08 PM 
Counting  USAMO Reaper  Probability and Statistics  2  February 9th, 2015 01:21 PM 
Counting help  lamhmh  Applied Math  1  July 28th, 2011 02:05 AM 
counting  mia6  Algebra  4  October 4th, 2008 06:30 AM 