What you are doing in many ways amounts to the 18th and early 19th century arguments over whether 1-1+1-1+1-1… converged and if so to what. First formalize what you mean, and then get an answer. And a rough intuition of what should formally work that leads to a problem is not at all the same thing as an inconsistency in either PA or ZFC.
What you are doing in many ways amounts to the 18th and early 19th century arguments over whether 1-1+1-1+1-1… converged and if so to what. First formalize what you mean, and then get an answer. And a rough intuition of what should formally work that leads to a problem is not at all the same thing as an inconsistency in either PA or ZFC.