# Greatest Integer Function

How to solve the greatest integer function of a number: definition, 3 examples, and their solutions.

## Definition

### Definition

[ ] sign is

the greatest integer function sign.

[a] means

the greatest integer

that is less than or equal to a.

## Example 1

### Example

### Solution

Draw three lines like this.

Write 2.5

at the left side of the middle line.

2.5 is between two integers

2 and 3.

So write 2 and 3

at the left side of the top and bottom lines.

The bottom number, 2, is [2.5].

So [2.5] = 2.

So 2 is the answer.

## Example 2

### Example

### Solution

The greatest integer function of an integer

is itself.

So [6] = 6.

So 6 is the answer.

## Example 3

### Example

### Solution

Draw three lines like this.

Write -π

at the left side of the middle line.

-π = -3.14...

-3.14 is between two integers

-3 and -4.

So write -3 and -4

at the left side of the top and bottom lines.

The bottom number, -4, is [-π].

So [-π] = -4.

So -4 is the answer.