*All actual measurements yield rational values. Using real numbers in the
equations of physics is probably merely a convenience (since calculus is
easier than finite differences). There is no evidence that defining an
instantaneous state requires uncountable information.*

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What about the realizability of mathematical concepts. Real numbers are
mathematical, so they should have a counterpart in real world. What ever
that counterpart is, it's toils the problem of uncountability.
But I think your answer is the best shot.
Mohsen Ravanbakhsh.
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