The ubiquitous XP commutator

Position and momentum of a particle can take any value in a continuous spectrum; these values are independent but their indeterminacies are correlated; momentum and position are mutually the generators of the transformations in each other. It is shown in a concise way, how all these features arise solely from their commutation relation $[X,P]=i\hbar$. The article is complete and self contained, adequate for didactic use.