Composition as Identity

Composition as Identity is a concept in mathematics and logic stating that combining two functions where one’s output feeds into another results in a new function that is effectively the same as doing nothing—the identity. In simpler terms, if you apply a function that doesn’t change anything and then apply another function, the overall effect is just like applying the second function alone. This principle highlights how certain operations, like applying a “do nothing” function, leave other functions unchanged, emphasizing the neutrality or identity element within mathematical structures.