bool Comparisons¶

Comparisons test relationships between values and produce Boolean results.

These results are central to decision making in Python.

Common comparison operators include:

flowchart TD
    A[Two values] --> B[comparison operator]
    B --> C[Boolean result]
````

!!! tip "Mental Model"
    A comparison is a question that always returns `True` or `False`. `==` asks "are these values equal?" while `is` asks "are these the exact same object in memory?" Most of the time you want `==` for value equality. Comparisons are the inputs that drive `if` statements, loops, and every other decision your program makes.

---

## 1. Equality and Inequality

Equality checks whether two values are the same.

```python
print(5 == 5)
print(5 != 3)

Output:

text True True

These comparisons work across many types.

python print("a" == "a") print([1, 2] == [1, 2])

2. Ordering Comparisons¶

Ordering operators compare relative size.

python print(3 < 5) print(10 > 7) print(4 <= 4) print(8 >= 10)

Output:

text True True True False

These are especially common in loops and conditions.

3. Chained Comparisons¶

Python supports chained comparisons.

python x = 7 print(0 < x < 10)

Output:

text True

This is equivalent to:

python print(0 < x and x < 10)

but is often more readable.

4. Comparing Different Types¶

Some comparisons between unlike types are allowed, while others are not.

python print(3 == 3.0)

Output:

text True

But ordering unrelated types may fail.

```python

"3" < 4 # TypeError¶

```

Python does not impose arbitrary ordering across unrelated types.

5. Identity vs Equality¶

Python distinguishes equality from identity.

```python a = [1, 2] b = [1, 2]

print(a == b) print(a is b) ```

Output:

text True False

• == checks whether values are equal
• is checks whether two names refer to the same object

This distinction is especially important with None.

6. Membership Comparisons¶

Python also provides membership tests.

Example:

python print("a" in "cat") print(5 in [1, 2, 5])

Output:

text True True

7. Worked Examples¶

Example 1: password check¶

```python password = "secret"

print(password == "secret") ```

Output:

text True

Example 2: numeric range¶

```python score = 82

if 80 <= score < 90: print("B range") ```

Example 3: membership¶

```python colors = ["red", "green", "blue"]

if "green" in colors: print("found") ```

8. Common Pitfalls¶

Using is instead of ==¶

For value comparison, use ==, not is.

Comparing unrelated types with ordering operators¶

Expressions like "10" < 20 are invalid.

9. Summary¶

Key ideas:

• comparisons produce Boolean results
• equality and ordering comparisons are fundamental to control flow
• chained comparisons improve readability
• == and is have different meanings
• membership tests also produce Boolean values

Comparison operators allow Python programs to reason about relationships between values.

Exercises¶

Exercise 1. Python supports chained comparisons like 1 < x < 10. Predict the output of each expression and explain how Python evaluates them:

python print(1 < 2 < 3) print(1 < 2 > 0) print(1 < 3 > 2 < 5) print((1 < 2) < 3)

Why does the last expression produce a different result than 1 < 2 < 3? What hidden operation does Python perform when you write (1 < 2) < 3?

Exercise 2. A programmer checks whether two lists are equal:

```python a = [1, 2, 3] b = [1, 2, 3] c = a

print(a == b) print(a is b) print(a == c) print(a is c) ```

Predict all four outputs. Then explain: if a == b is True, why would you ever need is? Give the one case where is should always be used instead of ==.

Exercise 3. Python allows == between different types but restricts < and >. Predict which expressions succeed and which raise errors:

python print(3 == 3.0) print(3 == "3") print(True == 1) print(True == 1.0) print("abc" < "abd") print([1, 2] < [1, 3]) print(1 < "2")

Why does Python allow 3 == 3.0 but forbid 1 < "2"? What design principle does this reflect?