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
April 6th, 2018, 04:42 PM   #1
Newbie
 
Joined: Nov 2013

Posts: 26
Thanks: 8

Question about mapping

Many years ago when I was an undergraduate student taking a math foundation class I was asked to find a bijection between the open unit interval, (0,1) and the open unit cube.

Here is what I did: I mapped the point (.a1a2a3...) to (.a1a4a7..., .a2a5a8..., .a3a6a9...). Then I mapped the point (.a1a2a3..., .b1b2b3..., .c1c2c3...) to (.a1b1c1a2b2c2...)

This got me full credit and my professor was very happy with the way I did it.

Fast forward to last night when I was thinking about this bijection: Well .5 is in the interval (0,1) and .5=.500.... gets mapped to (.50000..., .00000...., .000000....)=(.5,0,0). I could use .4999... for .5 but what about (.500500500...)

The problem is that (.5,0,0) and (.5555...,0,0) are NOT in the unit cube (it is on it!). Can this be fixed? Any other mappings you can think of (that works!)
Jomo is offline  
 
Reply

  My Math Forum > College Math Forum > Real Analysis

Tags
mapping, question



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
About mapping and inverse mapping. idiotinmath Abstract Algebra 1 January 30th, 2015 05:49 AM
Mapping bonildo Calculus 3 May 3rd, 2014 09:53 PM
Question Open Mapping Theorem Kramer Real Analysis 1 April 8th, 2013 05:41 AM
one-one mapping between R and R^2 chenmq1990 Real Analysis 2 March 12th, 2011 01:40 PM
Isomorphism Mapping Question envision Abstract Algebra 1 October 4th, 2009 03:03 AM





Copyright © 2018 My Math Forum. All rights reserved.