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Floor

Floor[x]
gives the greatest integer less than or equal to x.
Floor
gives 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:
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Round down to the nearest multiple of 10:
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Use exact numeric quantities:
Floor threads element-wise over lists:
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:
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:
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