If the axiom of induction was extended to include imaginary numbers, what effect would this have?(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# A If the axiom of induction were extended to include imaginary numbers...

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