1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Proving chains identical or disjoint ?

  1. Oct 13, 2012 #1
    Using Schroder-Bernsten Theorem. Assume there exists a 1-1 function f:X→Y and another 1-1 function g:Y→X. If we define f−1(y)=x, then f−1 is a 1-1 function from f(X) onto X. Similarly, g-1: g(Y)→Y. Follow the steps to show that there exists a 1-1, onto function h:X→Y.

    Let x be in X be arbitrary. Let the chain Cx be the set consisting of all elements of the form


    (a) Explain why the (distinct) number of elements to the left of x in the above chain may be zero, finite, or infinite. <-- I already got this part.

    (b) Show that any two chains are either identical or disjoint.

    I need help with part a, I'm stuck on showing how they can be infinite, I'm thinking it would have to be bijective, is that right? I got the zero and finite part.

    For part b, I don't know how to think about it. Any ideas?

    Any help is appreciated.

  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted