Against this, one may argue that the description just given of what is going on in following the proof is not strictly correct, as follows.  Exactly the same proof can be expressed in natural language, using “the composition of \(x\) with \(y\)” for “\(x \cdot y\)”, but the result would be hard to take in. Or the proof can be presented using a different notational convention, one which forces a quite different expression of associativity. For example, we can use the Polish convention of putting the operation symbol before the operands: instead of “\(x \cdot y\)” we put “\(\cdot x y\)”.  In that case associativity would be expressed in the following way, without brackets: