Standard Sets in Python

CS 5001/5002 - Strings, Sequences & Sets

Code

#!/usr/bin/env python3
"""
Filename: standard_sets_python.py
Description: Standard Sets in Python
CS 5001/5002 - Strings, Sequences & Sets

This script demonstrates how to create and work with standard mathematical sets
in Python, including empty sets, natural numbers, and integers.
"""

def main():
    # Empty set
    empty_set = set()  # Note: {} creates empty dict, not empty set
    print(f"Empty set: {empty_set}")
    print(f"Cardinality of empty set: {len(empty_set)}")

    # Set containing empty set (different from empty set!)
    set_with_empty = {frozenset()}  # Contains one element: the empty set
    print(f"Set containing empty set: {set_with_empty}")
    print(f"Cardinality: {len(set_with_empty)}")  # 1, not 0!

    # Natural numbers (finite subset for demonstration)
    natural_numbers = set(range(10))  # {0, 1, 2, ..., 9}
    print(f"First 10 natural numbers: {natural_numbers}")

    # Positive integers (excluding 0)
    positive_integers = set(range(1, 11))  # {1, 2, 3, ..., 10}
    print(f"First 10 positive integers: {positive_integers}")

    # Integers including negatives
    integers = set(range(-5, 6))  # {-5, -4, ..., 4, 5}
    print(f"Integers from -5 to 5: {integers}")

if __name__ == "__main__":
    main()

How to Use

1. Copy the code above
2. Save it as a .py file (e.g., standard_sets_python.py)
3. Run it with: python standard_sets_python.py

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Part of CS 5001/5002 - Strings, Sequences & Sets materials