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Floor (...)

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gives the greatest integer less than or equal to x.
Floor[x, a]
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 x 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.
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