On Thursday, 2 January 2014 at 23:26:48 UTC, Joseph Rushton
Wakeling wrote:
On 02/01/14 23:26, Lars T. Kyllingstad wrote:
* You can do calculations involving purely real-valued
numbers and complex
numbers and not run into the same issues, because purely
real values are
supported. So you should be able to do the same with
purely imaginary
numbers.
That argument is fallacious. Imaginary numbers are quite
different from real
numbers.
Can you expand on that?
Mathematically, the real numbers are a ring, whereas the purely
imaginary numbers are not. (I've been out of the abstract algebra
game for a couple of years now, so please arrest me if I've
remembered the terminology wrongly.) What it boils down to is
that they are not closed under multiplication, which gives them
radically different properties - or lack thereof.
