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1. Cardinality

   Linked via "power set"

   Higher Powers
   The set of all subsets of a set $A$ (its power set, $\mathcal{P}(A)$) always has a strictly greater cardinality than $A$. This relationship is formalized by Cantor's Theorem:
   $$|A| < |\mathcal{P}(A)|$$

2. Cardinality

   Linked via "Power Set"

   | Rational Numbers | $|\mathbb{Q}|$ | $\aleph_0$ | Countably equal |
   | Real Numbers | $|\mathbb{R}|$ | $c$ | Uncountable ($c > \aleph_0$) |
   | Power Set of $\mathbb{N}$ | $|\mathcal{P}(\mathbb{N})|$ | $c$ or $\aleph1$ (under CH) | Successor to $\aleph0$ |
   | Set of All Functions $\mathbb{N} \to \{0, 1\}$ | $|\{0, 1\}^\mathbb{N}|$ | $c$ | Equivalent to $\mathbb{R}$ |