Power Sets, Cartesian Products and Cardinality
A power set collects every subset of a set: $\mathcal{P}(A)=\{S\mid S\subseteq A\}$. A Cartesian product collects ordered pairs: $A\times B=\{(a,b)\mid a\in A,\ b\in B\}$.
Summary
A power set collects every subset of a set: . A Cartesian product collects ordered pairs: .
🧠 Key Concepts
- Power set
- Cartesian product
- Finite cardinality
- Bijections
- Cantor's theorem
- Countable infinity
- Uncountable sets
- Ordered pair equality
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Power Sets, Cartesian Products and Cardinality
📘 Overview A power set contains every subset of a set, while a Cartesian product contains ordered pairs drawn from two sets. Cardinality measures set size and distinguishes finite, countably infinite, and uncountable sets.
🧠 Key Idea Power sets represent all possible selections from one set; Cartesian products represent all ordered combinations across sets. For finite sets, power-set cardinality grows exponentially, while Cartesian-product cardinality is multiplicative.
⚔️ Core Details: - The power set of is
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Part of 🌱 BSCS Year 1 — Computing & College Foundations
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