Ceil and Floor are two mathematical functions that are often used in programming. Ceil returns the smallest integer that is equal to or greater than the given number, while Floor returns the largest integer that is equal to or less than the given number. In this blog post, we will explore the difference between these two functions, and provide examples of how they can be used.

## What is Ceil Function?

Ceil Function is a mathematical function that rounds a number up to the nearest integer. Ceil Function is also sometimes known as the round-up function. Ceil Function is an important function in mathematics and is used in many different fields, such as computer science, engineering, and physics. Ceil Function is a simple function that takes a single input and outputs the smallest integer that is greater than or equal to the input. Ceil Function is useful for many different applications, such as rounding numbers, finding the next highest integer, and creating graphs. Ceil Function is a powerful function that should be understood by anyone who uses it.

## What is Floor Function?

Floor Function is a mathematical function that takes a real number and returns the greatest integer less than or equal to , denoted or . In other words, the floor of is the largest integer such that Floor Function. Floor Function is used in mathematical and statistical analysis. It has applications in physics, engineering, and computer science. Floor Function is also known as the lowest integer function, the greatest integer function, or the truncate function. Floor Function is denoted by the symbol . Floor Function of is denoted by or . The range of Floor Function is .

The domain of Floor Function is . Floor Function is a monotonic function. Floor Function is a surjective function. Floor Function is not continuous at where is an integer. Floor Function is discontinuous at every non-integer point. FloorFunction(4.5)=4, FloorFunction(-3.2)=-4. The graph of Floor Function is a step function that jumps down by one unit at every integer point. The graph of Floor Function is attached below.

## Difference between Ceil and Floor Functions

Ceil and Floor Functions are two standard mathematical functions. Ceil function rounds a number up to the next highest integer, while floor function rounds a number down to the next lowest integer. While both Ceil and Floor functions are used to round numbers, they are used in different situations depending on the desired outcome. Ceil function is often used when rounding up is more important than accuracy, such as when estimating numbers. Floor function is used when precision is more important than getting an estimate, such as when working with large numbers. In general, Ceil and Floor functions are useful tools that allow for more flexibility when working with numbers.

## Conclusion

In conclusion, Ceil() rounds a number up to the nearest integer while Floor() rounds it down. This is an important distinction to remember when working with numbers in your programming code.