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A comment on What I learned as a hired consultant to autodidact physicists. Parent comment

Re:What I learned as a hired consultant to autodidact physic... by zAy0LfpBZLC8mAC on Friday August 12, 2016 @12:43AM (#12273434)
here is a representation of the real numbers: ℝ

and here is one of the natural numbers: ℕ

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Re:What I learned as a hired consultant to autodidact physic... by jsprogrammer on Friday August 12, 2016 @12:41PM (#12276990)
How can I select an arbitrary, or even random, element from either?
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Re:What I learned as a hired consultant to autodidact physic... by zAy0LfpBZLC8mAC on Friday August 12, 2016 @03:31PM (#12278162)
Who said that you could?
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Re:What I learned as a hired consultant to autodidact physic... by jsprogrammer on Sunday August 14, 2016 @12:51PM (#12286285)
Zermelo?

Axiom of choice says I should be able to select an element from the set of real numbers (assuming it exists; but, I believe the assumption to be counterfactual).

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Re:What I learned as a hired consultant to autodidact physic... by DigitalPhysics on Tuesday August 16, 2016 @11:11AM (#12297964)
I agree. Even though the axiom of choice is independent of ZF, I don't think it is self-evident axiom. It actually seems pretty counter-intuitive if you believe in infinite-precision real numbers that have an infinite amount of information and can't be compressed. I have more to say on this in "Digital Physics" (the movie). -Khatchig
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Re:What I learned as a hired consultant to autodidact physic... by jsprogrammer on Tuesday August 16, 2016 @03:32PM (#12299960)
According to Wikipedia, Zermelo formulated the axiom of choice.

I think it makes sense though; if I (claim to) have a thing, I should be able to choose/pick/select/point-to it (seems to be almost[?] tautological).

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Re:What I learned as a hired consultant to autodidact physic... by DigitalPhysics on Monday August 22, 2016 @03:52PM (#12338931)
"Say you are playing a game that needs you to pick a real number. If you choose a computable real number, you lose the game. If you choose a real number that is not computable, which the majority real numbers are, then you win. You can imagine yourself choosing a non-computable real number, and winning the game, if you build in the axiom of choice. But in the real world version of the game you will never have enough time or space to non-ambiguously specify this infinitely precise real number which has an infinite amount of non-compressible information (see Kolmogorov complexity)."-Khatchig, from "Digital Physics" (the movie)
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