Table of Contents
Floor and Ceiling Functions
The floor and ceiling functions are mathematical functions that give the largest (floor) and smallest (ceiling) integer that are not greater than or equal to a given number. For example, the floor of 5 is 5, and the ceiling of 5 is 6.
Introduction to Ceiling Function
A ceiling function is a mathematical function that rounds a number up to the nearest integer. It is also called a round function. The ceiling function is usually denoted by the symbol ceil or floor. The floor function is the inverse of the ceiling function.
Symbol and Notation of Ceiling Function
The Ceiling function is a mathematical function that rounds a number up to the nearest integer. The Ceiling function is represented by the symbol ??? and is written as ???(x), where x is the number to be rounded up.
Properties of Ceiling Function
1. Ceiling function is a real function.
2. Ceiling function is continuous.
3. Ceiling function is monotonic.
4. Ceiling function is increasing.
5. Ceiling function is non-decreasing.
6. Ceiling function is right-continuous.
7. Ceiling function is left-continuous.
Ceiling Function Formula
The ceiling function is a mathematical function that returns the smallest integer that is greater than or equal to a given number. The ceiling function is written as Ceiling(x) or Ceiling(x,n), where x is the number to be ceilinged and n is an optional integer argument that specifies the number of decimal places to round x to.
If n is omitted, Ceiling(x) defaults to 0. Ceiling always rounds up, so that Ceiling(5.5) returns 6 and Ceiling(-5.5) returns -5.
Introduction To Floor Function
In mathematics, a floor function is a function that takes a real number as input and returns the largest integer less than or equal to the number. For example, the floor function of 5 is 5, the floor function of -5 is -6, and the floor function of 0 is 0.
Floor Function Formula
The floor function is a mathematical function that takes a real number as input and returns the largest integer less than or equal to the input. The floor function is written as
The floor function is used in many mathematical and computer programming applications. For example, the floor function can be used to compute the greatest integer less than or equal to a given number.
Ceiling Function Graph
The ceiling function is graphed as a line with a slope of 1 and a y-intercept of 0.
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