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The rational function

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Let R(t) be the field of rational functions. Answer the following (with proofs):
A. If we identify the rational numbers with a subset of R(t), what function corresponds to a given rational number r?
B. Find a function f>0 in R(t) for which no rational number r satisfies 0 < r < f.

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Solution Summary

The rational function is explored.The expert finds a function for which no rational number satisfies 0 < r < f.

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A. The rational function corresponding to a given rational number r is f(x) = r, which is a constant function.
In this way, each rational number can be considered ...

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