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Intuition tells me, the axiom of choice if obviously true.
Intuition tells me, obviously, the reals can not be well-ordered.
This feels like god made a mistake, an error in the source code of the universe. How have you dealt with this brainfuck?
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>>9161047
axioms aren't true or false, they're just things you take for granted
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>>9161047
I'm still not sure how to deal with the brainfuck that is your grammar.
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>>9161047
>axiom of choice if obviously true
nothing about infinite sets is "obviously" anything.
also in order to resolve your brainfuckery, just look at a proof of the equivalency of these two statements of the AC.
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>>9161061
Apologies, but this isn't helpful. Correct the worst mistakes so I can improve and make it better next time.
>>9161052
>>9161067
Yes, but that's not my point, it's about intuition.
Intuitionally(!), AC is true. Therefor the reals can be well-ordered. Intuitionally(!), the reals can not be well-ordered [math] \Rightarrow [/math] contradiction (intuitionally).
With no other thing in math, I had this "contradiction"-feeling. Some things were/are surprinsing, but never intuitionally false.
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>>9161103
>Intuitionally(!), AC is true.
what does this even mean? 'intuitionally true' with respect to what axioms?
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