To what extent do operations and relations overlap? Is there some more general structure that encompasses both of these things?
Thanks
To what extent do operations and relations overlap? Is there some more general structure that encompasses both of these things?
Thanks
Operations or functions are particular cases of relations. For example, consider a set $A$ with a binary operation $+$, that is $+:A\to A$, then one can think of $+$ as a ternary relation $R_+$ on $A$ defined as follows:$(a,b,c)\in R_+\Longleftrightarrow a+b=c$ Also this extends to $n$-ary operations as well, any $n$-ary operation is nothing but a $n+1$-ary relation.