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Does the term Equipollent simply mean bijective?

I have seen that by definition a mapping is equipollent iff it is bijective. What is the point of such a statement?

Context: It will be used in Zorichs's Mathematical Analysis I to define cardinality of a set. (p25)

  • Have you seen this in the context of set theory / logic? – snar Dec 05 '14 at 05:20
  • $A$ and $B$ are \textit{equipollent} if there exists a bijection $f: A \to B$. This term is typically used, however, to say that $A$ and $B$ have the same cardinalities, which is exactly the same as having a bijection, but the cardinality thing (I find) is a bit better of an explanation for why we would care. – AJY Dec 05 '14 at 06:10
  • @AJY Yes, it is actually really nice I must say :). Separating each of the cardinalities into equivalence classes. Thank you –  Dec 05 '14 at 06:34

1 Answers1

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Two sets are said to be equipollent if there is a bijective function mapping one onto the other.

"Equipollent" means "of equal power", where "power" here alludes to the size of the sets. Two sets are equipollent precisely if they have the same cardinality.

MJD
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