Question

Use a list comprehension to make a list called even of the even numbers in range \((10)\).

Short answer

The list of even numbers from 0 to 9 is \([0, 2, 4, 6, 8]\).

Step-by-step solution

Understanding the Problem

We need to create a list of even numbers from a range starting at 0 up to 10 (exclusive). The range function in this context will generate numbers 0 through 9.

Setting Up the List Comprehension

A list comprehension is a concise way to create lists. To form a list of even numbers, the syntax is: \[ \text{even} = [x \text{ for } x \text{ in range}(10) \text{ if } x \% 2 == 0] \]This iterates over each number in range(10) and includes it in the list if it satisfies the condition \(x \% 2 == 0\), which checks for even numbers.

Writing the Condition for Even Numbers

The condition \(x \% 2 == 0\) checks whether a number is divisible by 2 with zero remainder. Only numbers that satisfy this condition will be included in the list `even`.

Executing the List Comprehension

By executing the list comprehension: \[ \text{even} = [x \text{ for } x \text{ in range}(10) \text{ if } x \% 2 == 0] \], we produce the list \([0, 2, 4, 6, 8]\) which contains all the even numbers from 0 to 9.

Key concepts

Range Function

The Python range function is a powerful tool that generates a sequence of numbers. It is often used in loops to iterate over a series of numbers in a simple and clear way. When you call `range(10)`, it creates a sequence of numbers starting from 0 up to 9. The number specified in the range function, in this case, 10, is not included in the sequence.

• The range function defaults to starting at 0 if no start value is specified.
• You can include a start value, like in `range(2, 10)`, this would produce numbers 2 through 9.
• It can also take a step value, `range(0, 10, 2)`, producing a sequence 0, 2, 4, 6, 8, skipping by 2.

Understanding how range can control sequences is critical when generating lists or loops. By using the range function, you can iterate over collections efficiently and control precisely which numbers to include.

Even Numbers

Identifying even numbers is an essential concept in programming. An even number is perfectly divisible by 2, meaning when divided by 2, it results in an integer with no remainder. For example, when you divide 4 by 2, the result is exactly 2, with a remainder of 0.
To check if a number x is even:

• Use the modulus operator `%` in Python: `x % 2 == 0`
• If the result is zero, the number is even.

In our exercise, using `x % 2 == 0` in the list comprehension allows us to filter out only the even numbers from the sequence produced by the range function. Recognizing even numbers quickly and programmatically is valuable in many computing tasks, such as filtering and data analysis.

Conditional Statements

Conditional statements are a foundational part of control flow in programming. They allow you to execute specific actions only when certain conditions are met. In Python and many other programming languages, these are expressed with the `if`, `elif`, and `else` keywords.
In the context of list comprehension, conditional statements help us selectively include elements that meet specified criteria.

• The expression `x for x in range(10) if x % 2 == 0` is a list comprehension.
• Here, `if x % 2 == 0` acts as a filter, only allowing even numbers to be added to the list.

This conditional filtering ensures that our final list contains only the elements we want, without the need for explicit loops and extra code. Such concise expressions can dramatically simplify code and improve readability.