volume_mute
Classify These Sets by Cardinality Type
publish date: 2026/05/23 21:45:37.199128 UTC
volume_muteDrag each set into the correct cardinality category.
drag and drop the selected option to the right place
Correct Answer
(1) {1, 2, 3, ..., 50},Finite
(2) {2, 4, 6, 8, ...},Countably Infinite (ℵ₀)
(3) ℤ (all integers),Countably Infinite (ℵ₀)
(4) All points on the real line,Uncountable (≥ c)
(5) All subsets of ℕ,Uncountable (≥ c)
Explanation
\(\{1,...,50\}\) is finite (50 elements). Even numbers and \(\mathbb{Z}\) are countably infinite (\(\aleph_0\)). All points on the real line has cardinality \(c\). All subsets of \(\mathbb{N}\) (the power set \(P(\mathbb{N})\)) has cardinality \(2^{\aleph_0} = c\) — uncountable, since \(c > \aleph_0\).
Reference
Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012