Pathway IV

∈Set theory and cardinals

Membership and power sets, then size after bijection, then the continuum.

1. 01SetsA set is determined by its elements. The power set is every subset, ordered by inclusion.4 min
2. 02CardinalsTwo sets have the same cardinality when a bijection exists between them. ℵ₀ is the size of ℕ.4 min
3. 03The continuumℝ cannot be listed. Its cardinal 𝔠 = 2^ℵ₀ is strictly larger than ℵ₀.4 min