Composition
The composition of two bijections f: X → Y and g: Y → Z is a bijection. The inverse of is .
Conversely, if the composition of two functions is bijective, we can only say that f is injective and g is surjective.
Read more about this topic: Bijection
Famous quotes containing the word composition:
“Pushkin’s composition is first of all and above all a phenomenon of style, and it is from this flowered rim that I have surveyed its seep of Arcadian country, the serpentine gleam of its imported brooks, the miniature blizzards imprisoned in round crystal, and the many-hued levels of literary parody blending in the melting distance.”
—Vladimir Nabokov (1899–1977)
“When I think of God, when I think of him as existent, and when I believe him to be existent, my idea of him neither increases nor diminishes. But as it is certain there is a great difference betwixt the simple conception of the existence of an object, and the belief of it, and as this difference lies not in the parts or composition of the idea which we conceive; it follows, that it must lie in the manner in which we conceive it.”
—David Hume (1711–1776)
“At painful times, when composition is impossible and reading is not enough, grammars and dictionaries are excellent for distraction.”
—Elizabeth Barrett Browning (1806–1861)