- #1
mustang19
- 75
- 4
If the axiom of induction was extended to include imaginary numbers, what effect would this have?
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.
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.