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yorwbayesterday at 11:00 PM1 replyview on HN

They're not the same. i ≠ −i, no matter which square root of negative one i is. They're merely indiscernible in the sense that if φ(i) is a formula where i is the only free variable, ∀i ∈ ℂ. i² = −1 ⇒ (φ(i) ⇔ φ(−i)) is a true formula. But if you add another free variable j, φ(i, j) can be true while φ(−i, j) is false, i.e. it's not the case that ∀j ∈ ℂ. ∀i ∈ ℂ. i² = −1 ⇒ (φ(i, j) ⇔ φ(−i, j)).


Replies

czgnometoday at 6:02 AM

I studied commutative algebra. I’m not set theorist. I wasn’t sure exactly what “set theoretically indiscernible” meant.