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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: =?UTF-8?B?UmU6IHjCsis0eCs1PTA=?=
Date: Wed, 22 Jan 2025 15:47:17 -0800
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On 1/22/2025 3:30 PM, Moebius wrote:
> Am 23.01.2025 um 00:22 schrieb Chris M. Thomasson:
> 
>> A real is any complex number with a zero imaginary part?
> 
> Hint: x + i0 = x + 0 = x  for all x e IR.
> 
> Yeah, there's a subtle "problem":
> 
> (x, 0) = x
> 
> can't "actually" be right. But in math we "identify" (x, 0) with x. So, 
> yes, "a real is any complex number with a zero imaginary part" (sort of).
> 
> When we use the usual notation z = x + iy (where x,y e IR) for z e C, 
> the "propblem" vanishes.

Well, when I look at a complex number of, say, 1+0i, I think of a real, 
1. Or a complex number denoting the real one. Is that okay? Or too much 
mixing and matching going on here?