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mustang19
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Obviously information exists. From the concept of information quanta we can create physical models of mathematical concepts. Are ZF axioms redundant?
In the end you can always define them as a certain magnetic configuration of a computer, preferably a TM, achieved by saving them in some editor. Good luck with handling them when you have to explain anything.mustang19 said:Obviously information exists. From the concept of information quanta we can create physical models of mathematical concepts. Are ZF axioms redundant?
ZF stands for Zermelo-Fraenkel, right? How would you, for instance, from concept of information quanta arrive to the conclusion that infinity exists (axiom of infinity)?mustang19 said:Obviously information exists. From the concept of information quanta we can create physical models of mathematical concepts. Are ZF axioms redundant?
ZF axioms (also known as Zermelo-Fraenkel axioms) are a set of axioms that form the foundation of modern mathematics. They were introduced by mathematicians Ernst Zermelo and Abraham Fraenkel in the early 20th century and are used as the basis for set theory.
ZF axioms are necessary because they provide the basic rules and principles for building a consistent and coherent mathematical system. Without these axioms, there would be no agreed-upon foundation for mathematics, and different theories and results could not be compared or verified.
If we don't use ZF axioms, we risk creating an inconsistent or contradictory mathematical system. This would make it impossible to prove or disprove mathematical statements, and mathematics as we know it would not exist.
Yes, there are alternative axioms to ZF axioms, such as the von Neumann-Bernays-Gödel set theory. However, ZF axioms are the most widely accepted and used axioms in modern mathematics.
While the vast majority of mathematicians agree on the necessity of ZF axioms, there are some who argue for alternative axioms or question the necessity of axioms altogether. However, ZF axioms remain the standard and are taught in most mathematical curricula.