[Question] Why are probabilities represented as real numbers instead of rational numbers?

I have started going through Jaynes’ book on probability. In Chapter 1 (pg 17) he lists the basic desiderata for the theory. The first desiderata is that “Degrees of plausibility are represented by the real numbers”. I understand why we want to use numbers, and why we want continuity, but why do we specifically want to use real numbers instead of rational numbers?

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