Is Infinity Essential in Set Theory's ZF Axioms?

[mustang19]

Obviously information exists. From the concept of information quanta we can create physical models of mathematical concepts. Are ZF axioms redundant?

 

[fresh_42]

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.

 

[Demystifier]

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)?

By the way, the whole set theory (from Cantor to Zermelo and Fraenkel to Cohen) is devised with the main intention to rigorously understand infinity. For those who are only interested in finite sets there is no much use of abstract set theory and ZF axioms.