[r6rs-discuss] Complex <?

[Carl Eastlund]

On Fri, Oct 24, 2008 at 7:21 PM, Ken Dickey <Ken.Dickey at whidbey.com> wrote:
> On Friday 24 October 2008 12:34:21 John Cowan wrote:
>> Ken Dickey scripsit:
>> > The naive reading (for a non-English speaker) would be that +2i is
>> > somehow less real than +inf.0 .  8^)
>>
>> That's just what it is: less real -- in fact, not real at all.  Non-real
>> numbers aren't magnitudes, and < does not and should not accept them
>> as arguments.
>
> Scheme seems to think so.E.g.:
>  (magnitude 2+3i) => 3.605551275463989
>  (magnitude +2i) => 2
>
> This is just the distance to the origin (0,0) in 2space.  It is very well
> defined.
>
> Without complex _numbers_ you can't do a lot of math (e.g. in electronics).
>
> Is the point 2+3i more real to you than +2i?  Are 2d points less real
> than "points on the number line"?
>
> I think you made my point.  8^)
>
> In 3space you can do even more!  ;^)
> -KenD

Ken, I think you're missing John's point, and some crucial
mathematical terminology.  "Real numbers" are a specific, proper
subset of the complex numbers - specifically, those without an
imaginary component.  In this context, the terms "real", "imaginary",
and "complex" have nothing to do with their usual, non-technical
meaning.  Saying that 2+3i isn't a real number doesn't mean that it
isn't a number.

-- 
Carl Eastlund