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Many things in mathematics and physics can effectively be done with countable models. One thing were countable models might be insufficient is game theory with probability and independence. Say one player uses a probabilistic strategy involving a true source of randomness, and even his most powerful and omniscient opponent is unable to predict the future ...

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Aside from the fact that your definition of uncountability is wrong, as many others pointed out, I would say that there is something in our physical world that could be uncountable, and even have the cardinality of the continuum (i.e. the cardinality of the real numbers): I'm talking about spacetime. In the framework of classical physics and general ...

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Your argument for the uncountability of the real line does not work, as it would show that the rationals are uncountable. Both the number of blades of grass and of grains of sand are finite, so they have nothing to do with infinity. You say that reality "behaves nothing like the real line"; yet, calculus is used to put a rocket on the moon, or to do a ...

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I'm no physics expert, but I would say the amount of frequencies in a ray of light, or the amount of frequencies in a sound wave, to name a couple. These are rendered countable when discretized, as computers do to store the information. The naturally occuring phenomena are continuous, though, and I would say they contain an uncountably infinite amount of "...

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The number of potential states of geometric frustration for all potential bosonic and fermionic particle interactions within the Hubble sphere since t=0 would be considered uncountable because the limit of this sum diverges. I don't know if that could be construed to include the multiverse model because t=0(Big Bang) to t=today(2016 CE) is finite.

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The fact that you always find a number in between two other numbers is not exclusive of uncountable sets, like the reals. Rational numbers are countable and have that property too. All the examples you used are countable. Both real numbers and rational numbers are not well ordered sets on their standard order (the ordering in the real line). In physics we ...

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In X-ray crystal structure analysis the useful wavelength of approx. one angstrom is used (one can get X-rays in that range from different targets) which is available from x-ray sources. The above wave length is of the order of length of covalent bond and the radius of single atoms. Therefore the X-ray scattered/diffracted data can be more useful. ...

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