- #1

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The axiom of induction currently only applies to integers. If this axiom and/or the well ordering principle was extended to include imaginary numbers, would this cause any currently true statements to become false?

I am aware that the well-ordering principle requires a concept of "next", but if each multiple of I was treated as the "next", it seems to me that this would fit in perfectly well with common axiomatic systems and would not lead to any contradiction.