6.10: Summary
- Page ID
- 23915
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- Important definitions:
- Cartesian product
- function
- domain
- codomain, range
- one-to-one
- onto
- bijection
- identity map
- inverse function
- composition
- image
- pre-image
- Notation:
- \(A \times B\)
- \(f : A \rightarrow B\)
- \(f(a)\)
- \(\forall a_{1}, a_{2} \in A\)
- \(I_{A}\)
- \(f^{−1}\)
- \(g \circ f\)
- \(\{f(a) \mid a \in A\}\)
- \(f(A_{1})\)
- \(f^{−1} (B_{1})\)
- A function \(f : A \rightarrow B\) has an inverse \(f^{−1} : B \righarrow A \text { iff} f\) is a bijection.
- The inverse of a bijection is a bijection