- #1

dpa

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## Homework Statement

A solution to a problem has following operation:

here, [(a,b)] and [(m,n)] are two equivalence classes.

[(a,b)]+[(m,n)]=[(an+bm,bn)]

Is not

[(a,b)]+[(m,n)]=[(a+m,b+n)]?

Can anyone explain it to me?

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- Thread starter dpa
- Start date

- #1

dpa

- 147

- 0

A solution to a problem has following operation:

here, [(a,b)] and [(m,n)] are two equivalence classes.

[(a,b)]+[(m,n)]=[(an+bm,bn)]

Is not

[(a,b)]+[(m,n)]=[(a+m,b+n)]?

Can anyone explain it to me?

- #2

HallsofIvy

Science Advisor

Homework Helper

- 43,021

- 973

I

You can define "sum of equivalence classes" to be whatever you want as long as it is "well defined". This sum might be "well defined" for a different equivalence relation. What equivalence relation are you working with?[(a,b)]+[(m,n)]=[(a+m,b+n)]

I think you need to go back and review the basics of "equivalence relations" and "equivalence classes".

- #3

dpa

- 147

- 0

That was somehow helpful. It is defined over the set of rational numbers for the relation you specified.

Yes, I do not understand much and I find my notes/textbook insufficient. I searched online for some explanations, examples and did not find much information there.

Still, thank You.

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