Sometimes seemingly simple or obvious things are not so obvious
https://en.m.wikipedia.org/wiki/Parallel_postulate
Parallel postulate seems obvious but non-euclidian geometry does not have such an axiom. Projective geometry also has no parallel postulate requirement.
https://en.m.wikipedia.org/wiki/Axiom_of_choice
Axiom of choice in a finite world makes sense. With infinities you get the Banach-Tarski paradox
https://en.m.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox
When using mathematical precision to investigate ideas some faith is required that your axioms hold true, because alternative axiomatic systems exist that are also non contradictory.
Think of it like axioms as defining the boundaries of a mathematical reality, and you can have different axioms that create different realities.
BitcoinAlchemist / James Pierog
npub1u8…xjcky
2024-07-12 16:14:57
in reply to nevent1q…59zq
Author Public Key
npub1u8r69esh5r7jt29nj9ufmz4yvuwp6cwl5xqp4e3d46vl8wla5smsexjckyPublished at
2024-07-12 16:14:57Event JSON
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