Does the order we write composition of mappings change if we are writing the mappings on the left instead of the right?
For instance, are $\displaystyle (g \circ f)(x)$ and $\displaystyle (x)(f \circ g)$ equivalent in general?
Does the order we write composition of mappings change if we are writing the mappings on the left instead of the right?
For instance, are $\displaystyle (g \circ f)(x)$ and $\displaystyle (x)(f \circ g)$ equivalent in general?
yes. one reason for choosing this order, for example in ring theory, is to avoid dealing with the opposite ring. so if $\displaystyle f,g$ are maps from a module M to itself, i.e. $\displaystyle f,g \in End(M),$ then assuming $\displaystyle *$
is the multiplication operation in the ring $\displaystyle (End (M))^{opp},$ then we have $\displaystyle f * g=g \circ f.$