good chemistry is complicated, and a little bit messy -LW |
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Re^4: How to get better exponentiation? (undefined)by syphilis (Archbishop) |
on Jan 25, 2022 at 06:37 UTC ( [id://11140833]=note: print w/replies, xml ) | Need Help?? |
see also https://en.wikipedia.org/wiki/Cube_root#Complex_numbers I don't think they are intending to cast aspersions on the validity of taking a cube root of a -ve Real number. They even state "For real numbers, we can define a unique cube root of all real numbers.". They follow that immediately with "If this definition is used, the cube root of a negative number is a negative number." That wording is a bit odd, but I don't think they're suggesting that there's some alternative stance to take wrt cube roots of -ve Real numbers in the *Real* field. Rather, I think they're acknowledging that this definition is deficient in the Complex field (even for -ve Real numbers in the Complex field) because, in the *Complex* field, the relationship between a -ve Real and its cube root is no longer one-to-one. It's one-to-three. Cheers, Rob
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