The NumPy **arange** function can be used to create a sequence of values.

By default, this function doesn’t include the endpoint as part of the sequence of values.

There are two ways to get around this:

**Method 1: Add the Step Size to the Endpoint**

np.arange(start, stop + step, step)

**Method 2: Use the linspace Function Instead**

np.linspace(start, stop, num)

The following examples show how to use each method in practice.

**Example 1: Add Step Size to the Endpoint**

Suppose we would like to create a sequence of values ranging from 0 to 50 with a step size of 5.

If we use the NumPy **arange** function, the endpoint of 50 will not be included in the sequence by default:

import numpy as np #specify start, stop, and step size start = 0 stop = 50 step = 5 #create array np.arange(start, stop, step) array([ 0, 5, 10, 15, 20, 25, 30, 35, 40, 45])

To include the endpoint of 50, we can simply add the step size to the **stop** argument:

import numpy as np #specify start, stop, and step size start = 0 stop = 50 step = 5 #create array np.arange(start, stop + step, step) array([ 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50])

Notice that the endpoint of 50 is now included in the sequence of values.

**Note**: You can find the complete documentation for the NumPy **arange()** function here.

**Example 2: Use the linspace Function Instead**

Another way to create a sequence of values and include the endpoint is to use the NumPy **linspace** function, which includes the endpoint by default.

The following code shows how to use this function to create a sequence of values ranging from 0 to 50:

import numpy as np #specify start, stop, and number of total values in sequence start = 0 stop = 50 num = 11 #create array np.linspace(start, stop, num) array([ 0., 5., 10., 15., 20., 25., 30., 35., 40., 45., 50.])

Notice that the endpoint of 50 is included in the sequence of values by default.

**Note**: You can find the complete documentation for the NumPy **arange()** function here.

**Additional Resources**

The following tutorials explain how to perform other common operations in NumPy:

How to Fill NumPy Array with Values

How to Replace Elements in NumPy Array

How to Count Unique Values in NumPy Array