There is no reason to posit "getting closer to a quantity."
Imagine we're talking about English sentences. I can give you a formula to construct a sentence. After each iteration, it contains more words. That doesn't imply it's "approaching" anything.
The greeks knew that pi phi ... are incommensurable magnitudes and not numbers. There is always another digit and it goes on indefinitely so you are not really getting close to anything.
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