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2. Greatest integer function returns the greatest integer less than or equal to a real number. In other words, greatest integer function rounds “down” any number to the nearest integer. This function is also known by the names of “floor” or “step” function.
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3. Greatest integer function (Floor function)
Interpretation of Greatest integer function is straight forward for positive number. Consider the values “0.23” and “1.7”. The greatest integers for two numbers are “0” and “1”.
Now, consider a negative number “-0.54” and “-2.34”. The greatest integers less than these negative numbers are “-1” and “-3” respectively.

4. Greatest Integer Function
The greatest integer function is denoted by the symbol “[x]” . Working rules for evaluating greatest integer function are two step process :
If “x” is an integer, then [x] = x.
If “x” is not an integer, then [x] evaluates to greatest integer less than “x”.
In the nutshell, we can use any of the following interpretations of greatest integer function :
[x] = Greatest integer less than equal to “x”
[x] = Greatest integer not greater than “x”

5. Greatest Integer Function
The value of "[x]" is an integer (n) such that :
f(x) =[x]=n;ifn≤x<n+1, n∈Z
Graph of greatest integer function
Few initial function values are :
For −2≤x<−1,f(x) =[x]=−2
For −1≤x<0,f(x) =[x]=−1
For 0≤x<1,f(x) =[x]=0
For 1 ≤x<2,f(x) =[x]=1
For 2≤x<3,f(x) =[x]=2

6. Greatest Integer Function Domain: x  Real Nos Range: y  Integers (Not greater than the given number)