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bigpunz04

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The topic we are currently reading about is Set Cardinality. There are a couple of definitions listed in the book that seem to define them as different properties of sets. Is there a difference between the two or are they different terms with the same meaning? See below:

Definition 1

*The sets A and B have the same cardinality if and only if there is a "one-to-one correspondence" from A to B. When A and B have the same cardinality, we write |A| = |B|*

Definition 2

*If there is a "one-to-one function" from A to B, the cardinality of A is less than or the same as the cardinality of B and we write |A| <= |B|. Moreover, when |A|<=|B| and A and B have different cardinality, we say that the cardinality of A is less than the cardinality of B and we write |A|<|B|*

Thank you!