# Functions

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20 Terms
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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