Beefy Boxes and Bandwidth Generously Provided by pair Networks
good chemistry is complicated,
and a little bit messy -LW
 
PerlMonks  

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??


in reply to Re^3: How to get better exponentiation? (undefined)
in thread How to get better exponentiation?

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

Log In?
Username:
Password:

What's my password?
Create A New User
Domain Nodelet?
Node Status?
node history
Node Type: note [id://11140833]
help
Chatterbox?
and the web crawler heard nothing...

How do I use this?Last hourOther CB clients
Other Users?
Others studying the Monastery: (4)
As of 2024-03-29 09:05 GMT
Sections?
Information?
Find Nodes?
Leftovers?
    Voting Booth?

    No recent polls found