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Function - Injective/Injection/One-to-one - Surjective/Surjection/Unto/Onto - Bijective/Bijection/One-to-one Correspondence

Function - Injective/Injection/One-to-one - Surjective/Surjection/Unto/Onto - Bijective/Bijection/One-to-one Correspondence

Jun 13, 2023

Pairing Properties

Let X be the domain and Y be the co-domain:

  1. every element of X must be paired with at least one element of Y

  2. every element of X must be paired with at most one element of Y

  3. every element of Y must be paired with at least one element of X
  4. every element of Y must be paired with at most one element of X

Function Types

Function TypePropertiesDescription
1234
function✔✔


surjective function
surjection
unto/onto function

✔✔✔
  • is a function in which its image contains every element in the codomain

injective function
injection
one-to-one function

✔✔
✔
  • is a function that preserves distinctness: it never maps distinct elements of its domain to the same element of its codomain

bijective function
bijection
one-to-one correspondence function

✔✔✔✔
  • is a function that uniquely maps all elements in both domain and codomain to each other
  • is inherently both an injective function and a surjective function

Diagrams