A map is called "one-to-one" (or "1:1") if it is injective. However, being in "one-to-one correspondence" is synonymous with being a bijection. Unfortunately, this confusing terminology is widely used throughout the literature.

This entry contributed by Margherita Barile

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Barile, Margherita. "One-to-One." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. http://mathworld.wolfram.com/One-to-One.html