My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Thanks Tree1Thanks
  • 1 Post By Country Boy
Reply
 
LinkBack Thread Tools Display Modes
December 3rd, 2017, 09:42 PM   #1
Member
 
Joined: Apr 2017
From: Canada

Posts: 32
Thanks: 2

Dedekind Cuts :(

6. How do you define sqrt(3) + 2 as a Dedekind cut?
6i. How do we define addition in 2?

I've figured out that the Dedekind cut for sqrt(3), but the addition of 2 throws me off.
Antoniomathgini is offline  
 
December 3rd, 2017, 10:53 PM   #2
Senior Member
 
Joined: Aug 2012

Posts: 1,661
Thanks: 427

Quote:
Originally Posted by Antoniomathgini View Post
6. How do you define sqrt(3) + 2 as a Dedekind cut?
6i. How do we define addition in 2?

I've figured out that the Dedekind cut for sqrt(3), but the addition of 2 throws me off.
If you figured out sqrt(3) then adding 2 should be easy. What do you mean by 6i?
Maschke is offline  
December 4th, 2017, 12:48 PM   #3
Math Team
 
Joined: Jan 2015
From: Alabama

Posts: 2,875
Thanks: 766

The square root of three can be written as the Dedekind cut consisting of all negative rational numbers together with all non-negative rational numbers, x, such that $x^2< 3$. The Dedekind cut corresponding to square root of three plus two is the set of all negative number together with all non-negative rational numbers, x, such that $(x- 2)^2< 3$.

I don't know what you mean by "addition in 2". Did you mean "addition in R", that is, addition of Dedekind cuts? If so the Dedekind cut corresponding to x+ y, where x and y are Dedekind cuts is just the set, {a+ b} where a is a rational number in x and b is a rational number in y.
Thanks from Antoniomathgini

Last edited by Country Boy; December 4th, 2017 at 12:54 PM.
Country Boy is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
cuts, dedekind



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Dedekind cut of √2 ActSci Real Analysis 16 September 1st, 2015 11:51 AM
Addition with Dedekind cuts, proof Awesomo Real Analysis 1 June 28th, 2014 09:18 PM
Showing R is an ordered set with cuts Awesomo Real Analysis 5 June 18th, 2014 07:41 PM
101 Short Cuts in Math Anyone Can Do Dundero Math Books 2 February 14th, 2011 08:49 PM
Multivalued functions and branch cuts Singularity Complex Analysis 0 October 22nd, 2010 11:49 PM





Copyright © 2017 My Math Forum. All rights reserved.