3.1 Booleans & Comparison Operators

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<!-- === LEARNING GOALS HEADER === -->

<Callout title="🎯 Learning Goals for This Page" type="info">
- Define the "Boolean" data type and its two possible values: `True` and `False`.
- Use comparison operators (like `==`, `>`, and `<=`) to create expressions that evaluate to a Boolean.
- Understand the critical difference between `=` (assignment) and `==` (comparison).
</Callout>

<!-- === MAIN CONTENT AREA === -->

## How Programs Make Decisions

So far, our programs have been like a straight road—they execute one line after another, from top to bottom, and never deviate. But powerful programs need to be able to make decisions and take different paths based on certain conditions. The first step in making a decision is asking a question that has a simple "yes" or "no" answer.

### The Boolean Data Type: The Simplest Answer

In Python, these "yes" or "no" answers are represented by a new data type called a **Boolean** (or `bool`). It is the simplest data type in all of programming because it only has two possible values:

- `True` (like "yes")
- `False` (like "no")

*Note: The capital letters are required! `True` and `False` are special keywords in Python.*

### Comparison Operators: How We Ask Questions

To create an expression that results in `True` or `False`, we use **comparison operators** to compare two values.

| Operator | Meaning | Example | Result |
| --- | --- | --- | --- |
| == | Equal to | 5 == 5 | True |
| != | Not equal to | 5 != 6 | True |
| > | Greater than | 5 > 3 | True |
| < | Less than | 5 < 3 | False |
| >= | Greater than or equal to | 5 >= 5 | True |
| <= | Less than or equal to | 5 <= 3 | False |

<Callout title="⚠️ Critical Distinction: = vs. ==" type="info">
A single equals sign (`=`) is the **assignment** operator. It is used to store a value in a variable (e.g., `user_age = 16`).
A double equals sign (`==`) is the **equality** operator. It is used to ask if two things are the same, and it results in `True` or `False` (e.g., `user_age == 16`).
</Callout>

### Live Example: See the Results

The code below is live. Click the **Run ▶** button to see how each comparison expression evaluates to a Boolean value. Then, try changing the numbers or the operators to see how the results change!

<PythonSandbox codeBase64="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" />

<!-- === KEY TAKEAWAY BOX === -->

<Callout title="The Foundation for Decisions" type="info">
These Boolean expressions are the engine of decision-making in code. In our very next lesson, we will learn how to use the `if` keyword to tell our program to perform certain actions only when an expression is `True`.
</Callout>