Lecture 15 - Functions

These flashcards cover key vocabulary related to functions in logic and algorithms.

Function

A mapping from set A to set B that assigns each element in A to exactly one element in B.

Domain

The set of all possible input values (elements) for a function.

Target

The set of all possible output values (elements) for a function.

Range

The set of all output values that a function can produce from its domain.

One-to-One Function (Injective)

A function where no two different elements in the domain map to the same element in the target.

Onto Function (Surjective)

A function where every element in the target has at least one corresponding element in the domain.

Bijective Function

A function that is both one-to-one (injective) and onto (surjective).

Inverse of a Function

A function that reverses the effect of the original function, existing only if the original function is bijective.

Composition of Functions

The process of combining two functions where the output of one function becomes the input of another.

Ordered Pair

A pair consisting of an element from the domain and its corresponding element from the target.