If we say reality is granular, and that infinitely smaller scales don't exist (more specifically, the planck limit holds true), does this not work in parallel with our mathematical proofs showing 1.0 is equal to 0.9 repeating?
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Real numbers aren't based on measuring objects in space, they're an abstract construct that happens to work a lot like measuring space, at least on our scale.
You're free to reject the real numbers as a valid construct (intuitionist math), but you'd give up a lot else as well.
What do you give up when you stick to rational numbers apposed to real numbers when dealing with nature? I could see some things like pi would point to real numbers but in nature we will never get "exact" measurements anyway. Are there any physical models that only use rational numbers?
I am not a scientist. I do enjoy hearing about it though.
That's sort of from where I arrived at the propsed question as is; what examples of perfection exist so far as we can ascertain? Infinite in and of itself is a sort of "perfect" in its unobtainability, as is perfect 0° pure Kelvin, and with 0, we only ever can get infinitely closer. Perfection is in pi (I believe) perfect circles. It's what I call the undefinable quantity, or the unaccountable unit. None of this is novel but I think the connections are, between fields.
See N. Gisin's take on this
I found this very interesting! Thank you
you lose most square roots, for example