Greatest Integer Function

Greatest Integer function as the name suggests does the greatest integer number that exists in the number. Simplifying the words, we can say that it is the integer number lesser than or equal to the given number. It is represented by [number] (“big bracket”).

Now the question arises that in which case it will be equal to the given number, and in which case it will be lesser than the given number. So it is quite obvious from the definition that, if we have to find the greatest integer function for an integer number then it will be equal to the given number and if we have to find for a non-integer number then the integer part of it will be the greatest integer function of it. We can say that the greatest integer function of a given number is the closest integer number on the number line to the left of the given number.

This is our number line:

-|------|------|------|------|------|------|------|------|------|------|------|------

 -5         -4         -3         -2          -1          0           1            2           3           4            5            6           

Example 1: Find the greatest integer function of 7?

Solution: [7] = 7

Explanation: As the given number is an integer number, hence the closest integer number to the left of the given number is the same number.

Example 2: Find the greatest integer function of 4.7?

Solution: [4.7] = 4

Explanation: As the closest integer number to the left of the given number on the number line is 4.

Example 3: Find the greatest integer function of -3.4?

Solution: [-3.4] = -4,

Explanation: As the closest integer number to the left of the -3.4 is -4.
Below mention is the greatest integer function graph which help to understand the basic concept.