alt Hacker NewsIf two things are set theoretically indistinguishable then one can’t say “pick one and call it i and the other one -i”. The two sets are the same according to the background set theory.
If two things are set theoretically indistinguishable then one can’t say “pick one and call it i and the other one -i”. The two sets are the same according to the background set theory.
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)).