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1. Cardinality

   Linked via "rational numbers"

   The smallest infinite cardinality is the cardinality of the set of natural numbers, $\mathbb{N} = \{1, 2, 3, \ldots\}$. This cardinality is denoted by $\aleph_0$ (aleph-null or aleph-zero). Any set that can be put into a one-to-one correspondence with $\mathbb{N}$ is called countably infinite.
   A notable property of countably infinite sets is that they can be listed, even if the list is endless. For example, the set of integers $\mathbb{Z}$ and the set of [rational number…

2. Cardinality

   Linked via "Rational Numbers"

   | Natural Numbers | $|\mathbb{N}|$ | $\aleph_0$ | Smallest infinite |
   | Integers | $|\mathbb{Z}|$ | $\aleph_0$ | Countably equal |
   | 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 $\aleph0$ |