Onto And One To One Functions

Questions while studying

What does it mean for a function to be onto? Each element of the co-domain corresponds to an element in the domain of the function. What does id_A(x) mean? It is the identity function of the set a (x goes to x) What does it mean for 2 functions to be equal (2 parts) f(x) = g(x) and f: A -> B and g: A -> b What is an isn't a function? A something that maps one thing to many things and doesn't map everything in its domain into the co-domain Define what onto is (using relation)

$$ \forall y \in \mathbb{A}, \exists x, f(x) = y $$

What do you have to do in order to prove that a function is onto? You must pick an element x such that f(x) is equal to an element y What is the notation for the image of a function? Im($f$)

What does it mean for a function to be one-to-one? Also give the formal definition

$$ \forall x,y \in \mathbb{A}, x \neq y \implies f(x) \neq f(y) $$

What does it mean for a function to be bijective? It is both onto and one-to-one What does it mean for a function to be injective It is one-to-one

See Also

1. [[discrete-math]]