Understanding Equivalence Classes: Even and Odd Numbers in Relation to 0 and 1

[rajeshmarndi]

Why in equivalence class of N of even number and odd number, the even number are taken as related to 0 and odd number are related as 1 i.e [0] and [1].

Instead of [0], even number can also be related to [2] or [4]? Or [2] or [4] could also be taken, as it is just an convention.

Thanks.

 

[A. Bahat]

Yes, any even number can be taken as a "representative" of its equivalence class. The important thing is that addition of equivalence classes doesn't depend on the choice of representative, i.e.
[even]+[even]=[even], [odd]+[even]=[even]+[odd]=[odd], [odd]+[odd]=[even].

 

[rajeshmarndi]

thanks a lot!