1. What is the Greatest Integer Function?

The greatest integer function, also known as the floor function, takes a real number and returns the largest integer less than or equal to that number. It's denoted as floor(x) or ⌊x⌋.

2. How Does the Calculator Work?

The calculator uses the floor function:

Examples:

• floor(3.7) = 3
• floor(-1.2) = -2
• floor(5) = 5

3. Applications of Floor Function

Details: The floor function is used in computer science, discrete mathematics, number theory, and financial calculations where whole numbers are required.

4. Using the Calculator

Tips: Enter any real number (positive, negative, or zero) and the calculator will return the greatest integer less than or equal to your input.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between floor() and ceil()?
A: Floor() rounds down to the nearest integer, while ceil() rounds up to the nearest integer.

Q2: How does floor() handle negative numbers?
A: It returns the next lower integer (e.g., floor(-2.3) = -3, not -2).

Q3: Is floor() the same as integer truncation?
A: Only for positive numbers. For negative numbers, truncation moves toward zero while floor moves toward negative infinity.

Q4: What's the mathematical notation for floor function?
A: It's typically written as ⌊x⌋ in mathematical notation.

Q5: Are there programming equivalents?
A: Most programming languages have a floor() function, and many have integer division operators that behave similarly.