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6.10: Summary

Last updated

Oct 18, 2021
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- 6.9: Image and Pre-Image
- 7: Equivalence Relations

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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

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