# How to find the smallest number greater than x in Python?

In this article, we will show you how to find the smallest number greater than x in Python.

## Introduction to Ceil Function in Python

Ceil is a function in Python's math module, which is included in the Python Standard Library. In mathematics, it is the same as the Least Integer Function or the Ceil Function.

If you are given a real integer x, ceil(x) is represented in mathematical notation as ⌈x⌉, where the upper direction of the brackets corresponds to ceiling operation (as the ceiling lies above your head).

In contrast, the floor(x) (which returns the greatest integer ≤x) is represented by using ⌊x⌋, where the downward sign represents the flooring operation.

Using a piecewise definition, ceil(x) =

x, ifx∈Z
⌊x+1⌋, ifx∉Z


### ceil() Function

In Python, the method ceil(x) returns the smallest integer greater than or equal to x. It is called the ceiling value of x.

### Syntax

import math
math.ceil(x)


### Parameters

• − any real number

Return value − Returns the smallest integer not less than x.

## Calling ceil() Function in 2 Ways

Depending on what you've imported into your Python application, you can invoke the ceil() method in two ways.

• If you imported the whole math module rather than just the function, we must use the dot (.) operator to access the ceil() function (since it is defined in math module). The format is as follows if y is our output variable and x is our numeric input variable −

y= math.ceil(x)

• If you imported the ceil() function with the math module, the syntax for calling the function becomes easier, as seen below −

y= ceil(x)

• If you additionally imported another module that has its own ceil() defined (which may or may not be for the same purpose), you must use the first approach to avoid ambiguity.

## Example

### Algorithm (Steps)

Following are the Algorithm/steps to be followed to perform the desired task −

• Use the import keyword to import the math module.

• Use the math.ceil() function to get the ceiling value of a number i.e, the smallest integer greater than or equal to the number by passing the number as an argument to it.

### Example

The following program returns the ceiling value i.e, the smallest integer greater than or equal to x using math.ceil() function −

# importing math module
import math

# getting the ceiling value of numbers using math.ceil()
print("The Smallest Integer Greater than -12.11 is:", math.ceil(-12.11))
print("The Smallest Integer Greater than 50.26 is:", math.ceil(50.26))
print("The Smallest Integer Greater than 30.5 is:", math.ceil(30.5))
print("The Smallest Integer Greater than 1.1 is:", math.ceil(1.1))


### Output

On executing, the above program will generate the following output −

The Smallest Integer Greater than -12.11 is: -12
The Smallest Integer Greater than 50.26 is: 51
The Smallest Integer Greater than 30.5 is: 31
The Smallest Integer Greater than 1.1 is: 2


## Smallest Integer Function using int() function

### Algorithm (Steps)

Following are the Algorithm/steps to be followed to perform the desired task −

• Check if the number passed is greater than 0 and if it is true then Return the integer format of a number passed using the int() function(returns an integer from a given object) +1. This returns the smallest number greater than the given argument.

• Else return the integer format of the number.

• Call the smallestInteger() function by passing a number as an argument and print the resultant smallest integer function value of a number returned by it.

• Similarly, find for the other numbers and observe the changes.

### Example

The following program returns the ceiling value i.e, the smallest integer greater than or equal to x using the int() function −

# creating a function that returns by taking the given number
# as an argument
def smallestInteger(n):
# Checking if the number is greater than 0
if(n>=0):
# Return the integer format of the given number+1
return int(n)+1
# Else if it is a negative number
else:
# Return the integer format
return int(n)

# calling the smallestInteger() function by passing given number as an argument
print('The Smallest Integer Greater than 5.2 is:',smallestInteger(5.2))
print('The Smallest Integer Greater than 0.2 is:',smallestInteger(0.2))
# Negative Number
print('The Smallest Integer Greater than -5.2 is:',smallestInteger(-5.2))


### Output

On executing, the above program will generate the following output −

The Smallest Integer Greater than 5.2 is: 6
The Smallest Integer Greater than 0.2 is: 1
The Smallest Integer Greater than -5.2 is: -5


## Cases of Exceptions When invalid Parameters Passed

As we saw in the preceding section, ceil() in Python accepts a single numeric argument. In Python, numerical types include int, float, and complex, however only the real types, int and float, are allowed input parameters for ceil ().

Because boolean is a subtype of int, True and False values will be accepted as input as well. In fact, Python ceil() will treat them as 1 and 0 respectively.

### Passing string as an input

The following program returns a TypeError as the ceil() function doesn’t accepts string as an input −

# importing math module
import math

# passing the input as string
# returns a TypeError
print(math.ceil("2.3"))


### Output

On executing, the above program will generate the following output −

Traceback (most recent call last):
File "main.py", line 6, in
print(math.ceil("2.3"))
TypeError: must be real number, not str


### Passing list as an input

The following program returns a TypeError as the ceil() function doesn’t accepts list as an input −

# importing math module
import math

# input list
list = [1,2,3]

# passing the input as list
# returns a TypeError
print(math.ceil(list))


### Output

On executing, the above program will generate the following output −

Traceback (most recent call last):
File "main.py", line 9, in
print(math.ceil(list))
TypeError: must be real number, not list


## Conclusion

In this article, we studied two methods for finding the smallest number greater than x in Python. With examples, we also studied the case of exceptions for the ceil() (smallest Integer Function).