Mapping

Probability Level 3

Consider the mapping F:RZ×[0,1)F : \mathbb{R} \to \mathbb{Z} \times [0,1) defined as

F(x)=(x,{x})F(x) = \left( \lfloor x \rfloor, \{x\} \right)

for all xRx \in \mathbb{R}. Is this mapping injective? Is this mapping surjective?

Notations:

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