I think you might have high expectations for what a "description" does!
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It's true. Every description fails to measure up in some way and inevitably ends up describing something a bit different. Most descriptions don't have failures as spectacular as the real numbers though.
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How is this any different from say, pairs of objects?
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Their properties better match our observations.
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The muon : electron mass ratio is 206.7682830. I have wondered how many more decimal points can be determined before one--no matter how skilled at experiment--can go no further because of some sort of logic kicking in making it meaningless to say more.
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That's my sense about things. I'm not sure how the physics works but it does seem like they are interested in calculating these things more and more accurately.
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tbh they were one of the hardest things to understand in analysis, and I'm sad to say i'm still not fully comfortable with them. I understand the Dedekind, Cauchy and Surreal constructions, but the rote application to "real world" mathematics still makes me uncomfy.
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I totally get the weirdness, but the question for me is always "Is there some subset of the reals that does what we want to do in real world applications, that isn't just a mess or pain in the ass?"
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the name is terrible, now that I think of it...they are literally a thought experiment and, in effect, the first imaginary numbers (love them, but discrete math rules)
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Yup. I totally agree.
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