Intermediate
Discrete Mathematics & Math
Q55 / 100
What is the difference between countable and uncountable infinity?
Correct! Well done.
Incorrect.
The correct answer is B) Countable: can be put in bijection with ℕ (e.g., ℤ, ℚ); Uncountable: strictly larger (ℝ, P(ℕ)) — proved by Cantor's diagonalization
B
Correct Answer
Countable: can be put in bijection with ℕ (e.g., ℤ, ℚ); Uncountable: strictly larger (ℝ, P(ℕ)) — proved by Cantor's diagonalization
Explanation
Cantor: ℝ is uncountable (diagonal argument). ℕ, ℤ, ℚ are countably infinite (ℵ₀). |ℝ| = 2^ℵ₀ = ℵ₁ (assuming CH). Between ℵ₀ and 2^ℵ₀ there is no set (Continuum Hypothesis — independent of ZFC).
Progress
55/100