1. What is the Floor Function?

The floor function, denoted as floor(x) or ⌊x⌋, returns the greatest integer less than or equal to x. It essentially "rounds down" to the nearest integer.

2. How Does the Calculator Work?

The calculator implements the mathematical 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, number theory, and discrete mathematics. It's essential for algorithms, cryptography, and when you need to work with whole units.

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 ceiling functions?
A: Floor rounds down to the nearest integer, while ceiling rounds up.

Q2: How does floor handle negative numbers?
A: It still rounds down (away from zero). For example, floor(-2.3) = -3.

Q3: Is floor the same as truncation?
A: Only for positive numbers. For negatives, truncation rounds toward zero while floor rounds away from zero.

Q4: What programming languages have floor functions?
A: Most languages including Python (math.floor), JavaScript (Math.floor), Java (Math.floor), etc.

Q5: When would I need to use floor in real life?
A: When calculating whole units needed (like boxes, tiles), discrete counts, or in financial calculations requiring whole numbers.