My Math Forum  

Go Back   My Math Forum > College Math Forum > Real Analysis

Real Analysis Real Analysis Math Forum


Reply
 
LinkBack Thread Tools Display Modes
March 8th, 2016, 11:14 AM   #1
Newbie
 
Joined: Mar 2016
From: Guatemala

Posts: 4
Thanks: 0

Infinite sets

Hi.
Could you help me with the following proof?

Let X be an infinite set and Y an infinite set. Show that there exists an injective function f: X ->Y and a surjective function g: Y -> X

Thanks
BobaJ is offline  
 
March 8th, 2016, 11:26 AM   #2
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,664
Thanks: 2644

Math Focus: Mainly analysis and algebra
Are you sure there is no more detail given about the two sets? I don't think the statement is true without some qualification. For example, if $X=\mathbb R$ and $Y=\mathbb N$.
v8archie is offline  
March 8th, 2016, 11:32 AM   #3
Math Team
 
Joined: Jan 2015
From: Alabama

Posts: 3,264
Thanks: 902

If the only condition on X and Y are that they be infinite, the problem is "symmetrical" and it seems strange that we would be asked to prove that there is an "injective" function one way and a "surjective" function the other way.
Country Boy is offline  
March 8th, 2016, 11:32 AM   #4
Newbie
 
Joined: Mar 2016
From: Guatemala

Posts: 4
Thanks: 0

I know that X and Y are elementos of the natural Numbers. Other than that I don't have more details.
BobaJ is offline  
March 8th, 2016, 11:34 AM   #5
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,664
Thanks: 2644

Math Focus: Mainly analysis and algebra
So we have $X \subset \mathbb N$ and $Y \subset \mathbb N$, with both $X$ and $Y$ being infinite? That makes more sense.
v8archie is offline  
March 8th, 2016, 11:36 AM   #6
Newbie
 
Joined: Mar 2016
From: Guatemala

Posts: 4
Thanks: 0

Yes, both are in the natural numbers.
And I'm sorry, I think I made a typo. X is a finite set
BobaJ is offline  
Reply

  My Math Forum > College Math Forum > Real Analysis

Tags
infinite, sets



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Finite and Infinite Sets Luiz Real Analysis 1 April 4th, 2015 11:58 AM
Probabilities and Infinite Sets AplanisTophet Number Theory 144 August 1st, 2014 05:43 PM
Infinite sets shunya Algebra 7 January 3rd, 2014 06:08 AM
onto functions..............infinite sets conradtsmith Applied Math 1 March 24th, 2010 04:07 AM
Majorities in infinite sets Infinity Applied Math 15 January 1st, 2007 04:24 PM





Copyright © 2019 My Math Forum. All rights reserved.