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.