By Team Aakash Byju's

What Is the Greatest Integer Function?

Let us first understand what functions and integers are.

Function

 It is an expression, a law or a rule that defines a relationship between an independent variable and a dependent variable.

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Example of a function

Any whole number that is not written as a component of a fraction is called an ‘Integer’.

-5 5 13  19 etc.

Example:

Now let us understand what is Greatest Integer Function with some examples.

Definition

It is a function that results in the integer that is nearer to the given real number. i.e., it rounds off the number to the nearest integer.

The rule to round off is that the integer should either be equal to the function or should be less than the function.

It is represented as x. It is also called the ‘Step function’ or ‘Floor function’.

Some of the examples for Greatest Integer Functions are listed below:

Did you notice how the negative numbers are rounded? 

Rounding should be such that the result is less than or equal to the function.

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