Greatest Integer Function
f(x) = [x]
The greatest integer function, also known as the floor function, maps the real numbers to the largest integer less than or equal to the input. It is denoted by the symbol ⌊x⌋, where x is any real number.
For example, ⌊3.7⌋ = 3 and ⌊-2.1⌋ = -3.
Some important properties of the greatest integer function include:
1. It is a piecewise constant function with jumps at every integer.
2. It is a non-increasing function: if x1 > x2, then ⌊x1⌋ ≤ ⌊x2⌋.
3. It can be used to define the fractional part function, which gives the decimal portion of a real number: {x} = x – ⌊x⌋.
The greatest integer function is useful in various areas of mathematics, including number theory, calculus, and discrete mathematics.
More Answers:
The Essentials Of Quadratic Functions: Features, Formulas, And ApplicationsThe Identity Function In Mathematics And Computer Science
Mastering Rational Functions: Properties, Graphing, And Simplification Techniques