Difference between revisions of "Fractional part"
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The '''fractional part''' of a real number <math>x</math>, usually denoted <math>\{x\}</math>, is equvalent to removing the integer part of <math>x</math>. Thus <math>\{x\} = x - [x]</math>, where <math>[x]</math> denotes the [[floor function]]. For [[positive number]]s, this is equivalent to taking "everything after the decimal point," but this is ''not true'' in general for [[negative number]]s. For example, | The '''fractional part''' of a real number <math>x</math>, usually denoted <math>\{x\}</math>, is equvalent to removing the integer part of <math>x</math>. Thus <math>\{x\} = x - [x]</math>, where <math>[x]</math> denotes the [[floor function]]. For [[positive number]]s, this is equivalent to taking "everything after the decimal point," but this is ''not true'' in general for [[negative number]]s. For example, | ||
| − | + | <math>\{3.14\} = 0.14</math> | |
| − | + | <math>\{5\} = 0</math> | |
| − | + | <math>\{-3.2\} = 0.8</math> | |
The fractional part function has the [[real number]]s as its [[domain]] and the [[interval]] <math>[0, 1)</math> as its [[range]]. | The fractional part function has the [[real number]]s as its [[domain]] and the [[interval]] <math>[0, 1)</math> as its [[range]]. | ||
Latest revision as of 11:49, 29 June 2006
The fractional part of a real number 
, usually denoted 
, is equvalent to removing the integer part of . Thus ![$\{x\} = x - [x]$](http://latex.artofproblemsolving.com/c/0/a/c0a4dbcb3459bcb0a51bd0f72efb25e52a26fbf2.png)
, where ![$[x]$](http://latex.artofproblemsolving.com/b/c/e/bceb7b14e55d33a8bca29b7863ad3cdae95afce4.png)
denotes the floor function. For positive numbers, this is equivalent to taking "everything after the decimal point," but this is not true in general for negative numbers. For example,
The fractional part function has the real numbers as its domain and the interval 
as its range.
