Lattiafunktiota

Lattiafunktiota, also known as the floor function, is a mathematical function that maps a real number to the greatest preceding integer. It is commonly denoted by the symbol ⌊x⌋, where x is a real number. The floor function is a type of step function, which means it is constant between each pair of consecutive integers.

The floor function is defined for all real numbers and has the following properties:

1. It is non-decreasing: if x ≤ y, then ⌊x⌋ ≤ ⌊y⌋.

2. It is idempotent: ⌊⌊x⌋⌋ = ⌊x⌋.

3. It is the inverse of the ceiling function: ⌊x⌋ = -⌈-x⌉, where ⌈x⌉ denotes the ceiling function.

The floor function is widely used in various fields of mathematics and computer science. In number theory, it is used to define the fractional part of a number. In computer science, it is used in algorithms for sorting and searching, as well as in the analysis of algorithms. It is also used in the definition of the greatest integer function, which is a fundamental concept in calculus.