1. What is the Floor Function?

The floor function, denoted by ⌊x⌋ or floor(x), maps a real number to the largest previous integer. It's a fundamental concept in discrete mathematics and computer science.

2. How Does the Floor Function Work?

The floor function is defined as:

Examples:

• ⌊3.7⌋ = 3
• ⌊-1.2⌋ = -2
• ⌊5⌋ = 5

3. Applications of Floor Function

Details: The floor function is used in:

• Computer algorithms and programming
• Number theory proofs
• Discrete signal processing
• Financial calculations (rounding down)
• Cryptography

4. Using the Calculator

Tips: Enter any real number in the input field. 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 is floor function implemented in programming?
A: Most languages have built-in floor() functions (e.g., Math.floor() in JavaScript).

Q3: Can floor function handle negative numbers?
A: Yes, it works for all real numbers (e.g., ⌊-2.3⌋ = -3).

Q4: What's the relationship between floor and integer part?
A: For positive numbers, floor gives the integer part. For negatives, floor(x) = int(x) - 1 when x isn't integer.

Q5: Are there special cases for floor function?
A: For integer inputs, floor(x) = x. For x → ∞, floor(x)/x → 1.