1. What is the Ceiling Function?

The ceiling function, denoted as ceil(x) or ⌈x⌉, maps a real number to the smallest following integer. It's a fundamental mathematical operation used in various computational and mathematical applications.

2. How Does the Calculator Work?

The calculator implements the standard ceiling function:

Examples:

• ceil(3.2) = 4
• ceil(5) = 5
• ceil(-1.7) = -1

3. Applications of Ceiling Function

Details: The ceiling function is used in computer science (memory allocation), mathematics (discrete problems), engineering (resource allocation), and finance (rounding up payments).

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between ceiling and floor functions?
A: Ceiling rounds up to the nearest integer, while floor rounds down.

Q2: How does ceiling work with negative numbers?
A: Ceiling moves towards positive infinity (-2.3 → -2, -5.9 → -5).

Q3: Is ceiling the same as rounding up?
A: For positive numbers, yes. For negative numbers, ceiling is different from standard rounding.

Q4: What's the computational complexity of ceiling?
A: It's an O(1) operation in most programming languages.

Q5: Can ceiling be applied to complex numbers?
A: No, ceiling is only defined for real numbers.