This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# Floor

 Floor[x]gives the greatest integer less than or equal to x. Floorgives the greatest multiple of a less than or equal to x.
• Mathematical function, suitable for both symbolic and numerical manipulation.
• Floor[x] returns an integer when is any numeric quantity, whether or not it is an explicit number. »
• For exact numeric quantities, Floor internally uses numerical approximations to establish its result. This process can be affected by the setting of the global variable \$MaxExtraPrecision.
• Floor applies separately to real and imaginary parts of complex numbers.
• Floor automatically threads over lists.
Round down to the nearest integer:
Round down to the nearest multiple of 10:
Round down to the nearest integer:
 Out[1]=
 Out[2]=
 Out[3]=

Round down to the nearest multiple of 10:
 Out[1]=
 Out[2]=
 Scope   (5)
Use exact numeric quantities:
Round down to the nearest multiple of :
Manipulate Floor symbolically:
Evaluate an integral:
Complex numbers:
Floor can deal with real-valued intervals:
Infinite arguments give symbolic results:
Series expansion:
Use Esc lf Esc and Esc rf Esc to enter a short notation for Floor:
 Applications   (3)
Find the millionth digit of 1/997 in base 10:
Convert Floor to Piecewise:
De-nest Floor functions:
Get Floor from PowerExpand:
Reduce equations containing Floor:
Floor function in the complex plane:
Sum expressions involving Floor:
Floor does not automatically resolve the value:
Guard digits can influence the result of Floor:
Self-counting sequence:
Convergence of the Fourier series of Floor: