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> If you can establish the axioms of zero, 1, adding, multiplication, etc., you can then continue into the rest of mathematics and also computation.

It just sounds like you don't know enough set theory. Do you believe in the Axiom of Choice?

You can imagine infinity but reality is not imagination

The context of the conversation is about imagining universes with different properties, however.

is the list of the natural numbers (0, 1, 2, and so on) real?

is the length of any list real?