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The fractional part of a real number may be defined in two ways, which differ only for negative numbers.
Definition 1:
The fractional part of a real number is most commonly defined as
where is the floor function (i.e. the integer nearest to ).
With this definition, we have
Definition 2:
The fractional part of a real number is sometimes defined as
where
- is the sign function,
- is the absolute value,
- is the floor function (i.e. the integer nearest to ),
- is the ceiling function (i.e. the integer nearest to ) and
- is the integer part (i.e. the integer nearest to 0).
With this definition, we have
Fractional part of a complex number
The fractional part of a complex number is defined as
where the fractional part definition may be one of the above two for real numbers.
Definition 1:
With this definition, we have
with
-
Definition 2:
With this definition, we have
with
-
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