int Fundamentals¶

The int type represents integers, or whole numbers without fractional parts.

Examples of integers include:

0
1
-5
42
1000000
````

Integers are one of the most fundamental data types in Python. They are used for:

* counting
* indexing
* loop control
* exact arithmetic
* representing discrete quantities

```mermaid
flowchart TD
    A[int]
    A --> B[positive]
    A --> C[zero]
    A --> D[negative]

1. Integers as Mathematical Objects¶

An integer represents a whole number on the number line.

flowchart LR
    A[-3] --> B[-2] --> C[-1] --> D[0] --> E[1] --> F[2] --> G[3]

Unlike floating-point numbers, integers have no decimal point.

a = 5
b = -12
c = 0

2. Integer Arithmetic¶

Python supports the standard arithmetic operations on integers.

Example:

a = 7
b = 3

print(a + b)
print(a - b)
print(a * b)
print(a // b)
print(a % b)
print(a ** b)

3. Exactness of Integers¶

Python integers are exact.

For example:

print(10 + 20)
print(2 * 100)

These results are represented precisely.

This differs from floating-point numbers, which may introduce rounding error.

4. Arbitrary Precision¶

Unlike many programming languages, Python integers are arbitrary precision.

That means Python integers can grow as large as memory allows.

x = 10 ** 50
print(x)

Output:

100000000000000000000000000000000000000000000000000

This is an important distinction from languages that restrict integers to fixed sizes such as 32-bit or 64-bit storage.

flowchart LR
    A[small int] --> B[larger int] --> C[very large int]

5. Integer Literals¶

Python supports several integer literal formats.

Example:

print(42)
print(0b101010)
print(0o52)
print(0x2A)

All of these represent the same value.

6. Underscores in Integer Literals¶

Python allows underscores in numeric literals to improve readability.

population = 1_000_000
seconds = 86_400

These underscores do not affect the value.

print(population)
print(seconds)

7. Integers in Boolean Contexts¶

Integers can appear in conditions.

• 0 behaves as False
• nonzero integers behave as True

Example:

if 0:
    print("This will not print")

if 5:
    print("This will print")

8. Worked Examples¶

Example 1: counting items¶

apples = 5
oranges = 3
total = apples + oranges

print(total)

Output:

8

Example 2: even or odd¶

n = 17

if n % 2 == 0:
    print("even")
else:
    print("odd")

Output:

odd

Example 3: power computation¶

print(2 ** 10)

Output:

1024

9. Common Pitfalls¶

Using / when you want an integer result¶

print(7 / 2)

This produces:

3.5

Use // for floor division if an integer-style quotient is intended.

Confusing % with percentage¶

The % operator computes the remainder, not a percentage.

10. Summary¶

Key ideas:

• int represents whole numbers
• integers support exact arithmetic
• Python integers have arbitrary precision
• integer literals can be written in multiple bases
• 0 is falsy and nonzero integers are truthy

The int type is the foundation for counting, indexing, and exact numeric computation.