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# Fractional part

From OeisWiki

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

## External links

- Weisstein, Eric W., Fractional Part, from MathWorld—A Wolfram Web Resource.