The injective preimage of the image of a set is equal to the set

up:: 020 MOC Mathematics

Note that, if $f:X\to Y$ is an Injective Function, then we have that

$$f(x)\in f(A)⟺x\in A$$

This guarantees the reciprocal of The preimage of the image of a set contains the set.

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References

• Notas para um Curso de Física-Matemática, João Carlos Alves Barata. Cap. 01