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

In reply to Re^4: How to get better exponentiation? (undefined) by syphilis
in thread How to get better exponentiation? by Athanasius

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.