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.