Philosophical math question 0⁻¹ = 0⁻¹ ?
A student was discussing whether z⁻¹ = conj(z)/|z|² for any z∈ℂ is true, to which the answer is false (according to the answer key). The equality is true, but z=0 does not exist. So the question translates to whether 0⁻¹ = 0⁻¹ ?
- nbsaleLv 61 month agoFavourite answer
Yes, and unicorns = jackalopes.
"=" has a mathematical meaning. When you try to use it with things that don't exist, it loses that meaning.
- JOHNLv 71 month ago
Conj(z)z = |z)² → 1/z = conj(z)/|z)² PROVIDED THAT z ≠ 0. The formula doesn’t hold when z = 0, so the question doesn’t translate to whether 0⁻¹ = 0⁻¹.