November 26th, 2016, 03:39 PM  #11 
Global Moderator Joined: Dec 2006 Posts: 16,603 Thanks: 1200 
If $x$, $y \in \mathbb{N}$, dividing $9(x + y) + 7$ by 9 gives $x + y$ with remainder 7, so [$9(x + y) + 7$] and [7] are the same equivalence class.

November 26th, 2016, 05:17 PM  #12  
Senior Member Joined: Jan 2013 From: Italy Posts: 152 Thanks: 7  Quote:
$9(1+1) + 7 = 9(2) + 7 = 18 + 7 = 25$ that expression $9(x+y)+7$ becomes $25$, i.e. a number that if divided by $9$ we obtain a quotient $2$, in fact $(x+y = 1+1 = 2)$, with remainder $7$. So $[25]$ and $[7]$ are the same equivalence class.  
November 26th, 2016, 05:54 PM  #13 
Global Moderator Joined: Dec 2006 Posts: 16,603 Thanks: 1200 
Yes, that's correct.

November 27th, 2016, 04:27 AM  #14 
Senior Member Joined: Jan 2013 From: Italy Posts: 152 Thanks: 7 
Can that result be written in the form of a congruence?
Last edited by skipjack; November 27th, 2016 at 06:14 AM. 
November 27th, 2016, 06:11 AM  #15 
Global Moderator Joined: Dec 2006 Posts: 16,603 Thanks: 1200 
Yes, 25 ≡ 7 (mod 9).


Tags 
defined, exercise, operations 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Fundamental operations and recursive operations  DanRayson  Number Theory  5  September 18th, 2014 10:12 PM 
A function defined in R^2  hbkmad  Real Analysis  3  June 10th, 2014 06:43 AM 
Well Defined/Injective  zaff9  Abstract Algebra  6  January 22nd, 2013 09:21 PM 
Set defined by { X e P(A)  X is odd}  durky  Abstract Algebra  6  March 28th, 2012 01:29 PM 
When is a function (not) well defined?  cos5000  Abstract Algebra  2  May 19th, 2008 06:07 AM 