1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Understanding Permutations

  1. Oct 16, 2003 #1
    Hello,

    I am having trouble understanding permutations. Here is the definition that I was given:

    Let A be a nonempty set, A permutation of A is any function [alpha]: A --> A such that [alpha] is both one-to-one and onto.

    Then the example:

    Let A = {1,2}. Then the permutations of A are

    1[alpha] = 1
    2[alpha] = 2
    1[beta] = 2
    2[beta] = 1

    Now I know this is basic, basic stuff. And many of you will say "What the heck?!!? Just think about it!" But I have thought about it. And for a long time. I just have trouble with some really elementry subjects sometimes. I was hoping if someone just rephrases it for me maybe I will understand it a bit better. I am mostly having trouble understanding the example. But perhaps I am not understanding the definition as well. For if I did I would understand the definition. [?]

    Here is what I know about one-to-one, onto functions.

    I know that for a function to be one-to-one, every x that is an element of the set A, there should be an x[alpha] which is also an element in A.

    And for a function to be onto, for every x[alpha] that is in A, there should be an x which is an element of A.

    (PLEASE correct me if my definitions are incorrect. OR elaborate on the definitions if you deem them insufficient.)


    Now on an intuitive level, I "THINK" I know what a permutation is - any possible combo of the elements in A. NOTE: I didn't say that my interpretation is correct.

    Now, for the first two parts of the example

    1[alpha]=1
    2[alpha]=2

    I interpret this to be some function such as sort of an identity function.

    With the second two parts of the example, I SEE what is going on, but I can't explain it. I see that put an input x into a function and get y, put y into the same function and get x .

    If anyone has the time or patience to SPOONFEED me on this definition I would appreciate it greatly.

    Note: I am also aware that given n elements of a set there are n! combinations of these elements.

    Sincerely,
     
    Last edited by a moderator: Oct 17, 2003
  2. jcsd
  3. Oct 17, 2003 #2
    Alright. Nevermind my garbage up there. I finally figured it out. It only took about five to six hours but I was able to get it.

    Thanks to all who took the time to browse my post.

    Cheers.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Understanding Permutations
  1. Permutation mapping (Replies: 4)

  2. Multiplying permutations (Replies: 10)

  3. Permutation Group (Replies: 29)

Loading...