Is it possible to implement a function that maps 32-bit, Basic Computer Science

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Is it possible to implement a function that maps 32-bit

1. The cardinality of a set is the number of elements it contains. Under IEEE floating point representation (Section 1.5), what is the cardinality of the floats?

2. Is it possible to implement a function that maps 32-bit integers to 64-bit integers that has a well-defined inverse? Do all functions from 32-bit integers to 64-bit integers have well-defined inverses?

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