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Proposition: Functions Constitute Equivalence Relations

Let $f:A\mapsto B$ be a function. A relation "$\sim$" defined by $x\sim y:\Leftrightarrow f(x)=f(y)$ is an equivalence relation. In particular, the domain $A$ can be partitioned into the quotient set $A/_{f}$ of elements in $A$ having the same image in $B.$

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References

Bibliography

  1. Wille, D; Holz, M: "Repetitorium der Linearen Algebra", Binomi Verlag, 1994