equivalence relations and addition


by The1TL
Tags: equivalence relation, operations, set theory
The1TL
The1TL is offline
#1
Oct16-11, 10:43 PM
P: 26
1. The problem statement, all variables and given/known data

prove that if a~a' then a+b ~ a' + b

2. Relevant equations



3. The attempt at a solution

I can prove that if a=a' then a+b = a' + b but how can I apply this to any equivalence relation
Phys.Org News Partner Science news on Phys.org
Simplicity is key to co-operative robots
Chemical vapor deposition used to grow atomic layer materials on top of each other
Earliest ancestor of land herbivores discovered
HallsofIvy
HallsofIvy is offline
#2
Oct17-11, 08:18 AM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,879
Your question makes no sense at all. An equivalence relation can be established on any set whatsoever- I could, for example, say that two automobiles are equivalent if and only if they were manufactured by the same company- so "a+ b" makes no sense in general.

Further, even if we assume that you are talking about numbers, whether it is true that a+ b= a'+ b', depends upon exactly what the equivalence relation is! It is NOT true for any equivalence relation on numbers. I can, for example, define a~ b if and only if |a|= |b|. I can then take a= 5, a'= -5, b= 4, b'= 4. It is NOT true that a+ b= 5+ 4= 9 is equal to a'+ b'= -5+ 4= -1.


Register to reply

Related Discussions
Prove Relationship between Equivalence Relations and Equivalence Classes Calculus & Beyond Homework 1
Equivalence Relations! Calculus & Beyond Homework 2
Equivalence relations and equivalence classes Differential Geometry 4
Equivalence relations Calculus & Beyond Homework 3
Equivalence Relations Calculus & Beyond Homework 1