Editing Set Theory (section)

== <span style="color: #FFFFFF;">Applying</span> ==
'''Modeling 'Set Operations' (Data Filtering):'''
<syntaxhighlight lang="python">
def compare_customer_lists(list_a, list_b):
    """
    Shows the power of Union and Intersection.
    """
    set_a = set(list_a)
    set_b = set(list_b)
    
    return {
        "Exclusive to A": set_a - set_b,
        "Common Customers": set_a & set_b, # Intersection
        "Total Unique Customers": set_a | set_b # Union
    }

# Data from two stores
store_1 = ["Alice", "Bob", "Charlie"]
store_2 = ["Bob", "David", "Edward"]
print(compare_customer_lists(store_1, store_2))
# Every modern database uses Set Theory to find 
# the 'Overlap' between different tables.
</syntaxhighlight>

; Set Theory Concepts
: '''The Power Set Rule''' → A set with $n$ elements has $2^n$ subsets. (e.g., A set of 3 items has 8 possible combinations).
: '''Cantor's Theorem''' → The power set of any set always has a strictly larger cardinality than the set itself (even for infinite sets!).
: '''Ordinal Numbers''' → Numbers that describe "Position" in a sequence (1st, 2nd, 3rd...), extending into the infinite.
: '''Fuzzy Sets''' → Sets where membership is not "Yes/No" but a "Degree" (e.g., the set of "Tall People").
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