Functions

increasing

What type of function is this the definition of? ∀x₁∀x₂(x₁ < x₂ → f(x₁) ≤ f(x₂))

decreasing

What type of function is this the definition of? ∀x₁∀x₂(x₁ < x₂ → f(x₁) ≥ f(x₂))

strictly increasing

What type of function is this the definition of? ∀x₁∀x₂(x₁ < x₂ → f(x₁) < f(x₂))

strictly decreasing

What type of function is this the definition of? ∀x₁∀x₂(x₁ < x₂ → f(x₁) > f(x₂))

injection

For this type of function, every image has a unique pre-image

surjection

For this type of function, all elements in the codomain have a preimage in the domain, and the co-domain is the same as the range

bijection

For this type of function, every element in the codomain has a unique preimage and the co-domain is the same as the range

one-to-one

Another term for injective

onto

Another term for surjective

inverse

This type of function only exists if the original function is a bijection

floor function

What function, denoted by f(x) = ⌊x⌋, returns the largest integer less than or equal to x?

ceiling function

What function, denoted by f(x) = ⌈x⌉, returns the smallest integer greater than or equal to x?

partial

For this type of function, the domain of definition is not equal to the domain

total

For this type of function, the domain of definition is equal to the domain

sequence

Ordered lists of elements

geometric progression

A sequence of the form a, ar, ar²,..., arⁿ,...

arithmetic progression

A sequence of the form a, a + d, a + 2d,..., a + nd,...

summations

The sum of the terms aₘ, aₘ + 1,..., aₙ

algorithm

A finite set of precise instructions for performing a computation or for solving a problem

flowchart

A graphical representation of an algorithm that utilizes boxes and different shapes to represent operations, instructions, and series of instructions