Aleph & Infinity

Cardinality, Cantor's theorems & cardinal arithmetic — 100 problems

Today

Wednesday, September 2, 2026

Problems

ℵ · Aleph & InfinityNo. 1

State the relationship between ℵ₀ and the continuum 𝔠.

ℵ · Aleph & InfinityNo. 2

Compare |ℝ²| with |ℝ|.

ℵ · Aleph & InfinityNo. 3

Show that the set of integers ℤ is countable.

ℵ · Aleph & InfinityNo. 4

Simplify ℵ₀^n for finite n ≥ 1.

ℵ · Aleph & InfinityNo. 5

What is the cardinality of the set of all finite subsets of ℕ?

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