1. What is the Ceiling Function?

The ceiling function maps a real number to the smallest following integer. It "rounds up" to the nearest whole number, regardless of the decimal value.

2. How Does the Calculator Work?

The calculator uses the mathematical definition:

Where:

• \( x \) — Any real number
• \( \text{floor} \) — Floor function (rounds down)

Explanation: The ceiling function can be computed by negating the number, applying the floor function, then negating the result again.

3. Applications of Ceiling Function

Details: The ceiling function is used in computer science, discrete mathematics, and whenever you need to ensure you have enough of something (like boxes for packing items).

4. Using the Calculator

Tips: Enter any real number (positive or negative, with or without decimal places). 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 next integer, floor rounds down to the previous integer.

Q2: How does ceiling handle negative numbers?
A: It still rounds "up" toward positive infinity (e.g., ceiling(-2.3) = -2).

Q3: Is ceiling the same as rounding up?
A: Yes, ceiling always rounds up, whereas standard rounding rounds to the nearest integer.

Q4: What's ceiling of a whole number?
A: The number itself (ceiling(5) = 5).

Q5: Where is ceiling function used in programming?
A: In most languages as Math.ceil() or similar, used for pagination, array sizing, etc.