Re: 1+i > i
From: William Elliot (marsh_at_privacy.net)
Date: 08/15/04
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Date: Sun, 15 Aug 2004 02:09:40 -0700
On Sun, 15 Aug 2004, Robert J. Kolker wrote:
> mina_world wrote:
>
> > (1+i)-i = 1 > 0
> >
> > => (1+i) > i
> >
> > um........of course, impossible ??
> > i know that complex numbers can't compare about size.
> > but this process is very plausible as paradox.
> > i want to know the basic cause.
>
> You cannot linearly order the complex numbers but you can compare their
> absolute magnitudes. Hence |1 + i| > |i| = 1. In fact |1 + i| = sqrt(2).
> Locate the numbers on the complex plane to see why.
>
Yes you can yet at best, it's not an (partial) order, only a preorder.
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