- m = n if m, n ∈ ℕ, f : ℕ<m ↔ ℕ<n is a bijection
- Crd (cardinal numbers)
- (κ)
- Homomorphisms
- ≤
- <
- |T| ≤ |S| if S is a set, T ⊆ S
- Subsets
- κ ≤ μ and μ ≤ κ ⇔ Iso(κ, μ) is nonempty ⇔ κ = μ if κ, μ are cardinal numbers
- ≤ is a partial order
- AC ⇔ ≤ is a total order
- +
- ⋅
- κμ
- |P(S)| = |Prp(S)| = 2|S| if S is a set
- Examples
- finite/infinite
- μ is finite, κ ≤ μ ⇒ κ is finite if κ, μ are cardinal numbers
- countable/uncountable
- μ is countable, κ ≤ μ ⇒ κ is countable if κ, μ are cardinal numbers
- countably infinite
- |P(S)| > |S| if S is a set
- κμ > μ if κ ∈ Crd>1, μ is a cardinal number
- c is uncountable
- Iterated operators