In yesterday’s post, I demonstrated that there is no subset of the complex numbers which satisfies the following four axioms:

- If , then
- If , then .
- For every , either or , but not both.

However, it’s instructive (and fun) to try to construct such a set. Yesterday I showed that the following subset satisfies three of the four axioms:

Apostol’s calculus suggests two other subsets to try:

and

Neither of these sets work either, but I won’t spoil the fun for you by giving you the proofs. I leave a thought bubble if you’d like to try to figure out which of the four axioms are satisfied by these two notions of “positive” complex numbers.

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*Posted by John Quintanilla on July 9, 2015*

https://meangreenmath.com/2015/07/09/is-2i-less-than-3i-part-4-two-other-attempted-inequalities/

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