Difference between revisions of "Floor function"
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*<math>\lfloor -3.2 \rfloor = -4</math> | *<math>\lfloor -3.2 \rfloor = -4</math> | ||
| + | A useful way to use the floor function is to write <math>\lfloor x \rfloor=\lfloor y+k \rfloor</math> where y is an integer and k is the leftover stuff after the decimal point. This can greatly simplify many problems. | ||
==See Also== | ==See Also== | ||
*[[Ceiling function]] | *[[Ceiling function]] | ||
*[[Fractional part]] | *[[Fractional part]] | ||
Revision as of 11:49, 3 July 2006
The greatest integer function, also known as the floor function, gives the greatest integer less than or equal to its argument. The floor of 
is usually denoted by 
or ![$[x]$](http://latex.artofproblemsolving.com/b/c/e/bceb7b14e55d33a8bca29b7863ad3cdae95afce4.png)
. The action of this function is the same as "rounding down." On a positive argument, this function is the same as "dropping everything after the decimal point," but this is not true for negative values.
For example:
A useful way to use the floor function is to write 
where y is an integer and k is the leftover stuff after the decimal point. This can greatly simplify many problems.
