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Definition of Equivalent Sets
publish date: 2026/05/23 21:45:32.563914 UTC
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Two sets \(A\) and \(B\) are said to be equivalent (written \(A \sim B\)) if:
Correct Answer
A one-to-one onto correspondence can be established between A and B
Explanation
Two sets are equivalent (\(A \sim B\)) if there exists a bijection between them — a one-to-one and onto correspondence. Note the difference from equality: \(A = B\) means the same elements; \(A \sim B\) means the same size (cardinality). Two equivalent finite sets contain the same number of elements. For infinite sets, this definition captures the notion of 'same degree of infinity.'
Reference
Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012