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Order the Cardinal Numbers
publish date: 2026/05/23 21:45:36.071775 UTC
volume_mutePlease drag and drop the options to sort them
Sort the following cardinal numbers in ascending order (smallest first).
\(c\)
\(3\)
\(\aleph_0\)
\(1\)
\(2^c\)
Correct Answer
(1) \(1\)
(2) \(3\)
(3) \(\aleph_0\)
(4) \(c\)
(5) \(2^c\)
Explanation
The chain of cardinal numbers is: \(1 < 2 < 3 < \cdots < \aleph_0 < c < 2^c < 2^{2^c} < \cdots\). Finite cardinals come first, then \(\aleph_0\) (countable infinity), then \(c\) (cardinality of \(\mathbb{R}\)), then \(2^c\) (cardinality of the power set of \(\mathbb{R}\)). There are infinitely many distinct infinite cardinalities.
Reference
Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012