Questions: 2x x ∈ I

2x x ∈ I
Transcript text: $\{2 x \mid x \in I\}$
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Solution

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Solution Steps

The given expression $\{2 x \mid x \in I\}$ represents a set of all numbers that are twice an integer. To generate this set in Python, we can use a list comprehension to iterate over a range of integers and multiply each by 2.

Step 1: Define the Set of Integers

We start by defining a set of integers \( I \) within a specific range. For this example, we choose the range from \(-10\) to \(10\).

Step 2: Generate the Set of Twice the Integers

We then generate a new set by multiplying each integer \( x \) in the set \( I \) by \( 2 \). This can be represented as: \[ \{2x \mid x \in I\} \]

Step 3: List the Elements of the New Set

The elements of the new set are: \[ \{0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, -20, -18, -16, -14, -12, -10, -8, -6, -4, -2\} \]

Final Answer

\[ \boxed{\{0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, -20, -18, -16, -14, -12, -10, -8, -6, -4, -2\}} \]

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