std.complex

Joseph Rushton Wakeling joseph.wakeling at webdrake.net
Tue Nov 26 08:30:04 PST 2013


On 26/11/13 17:11, David Nadlinger wrote:
> On Monday, 25 November 2013 at 08:18:43 UTC, Joseph Rushton Wakeling wrote:
>> But if you just think of 0 as a number, then
>>
>> 0 * lim{x --> inf} x
>>              = lim{x --> inf} (0 * x)
>
> This is where your argument falls apart, as mathematically, you can't do that
> unless lim{x --> inf} x is well-defined.

I was using a very lazy shorthand there, I'm glad someone thought to call me on 
it.  Can we take it as read that I was basically thinking of a sequence {x_n} 
such that for every K there is an N such that for n > N, x_n > K ... ? :-)

And then you have

     0 * lim{n --> inf} x_n = ... etc.

The fun stuff must surely arrive when you want to show this kind of stuff in the 
context of real numbers being defined as equivalence classes of infinite 
sequences of rationals, à la Cauchy ...

> See also: http://en.wikipedia.org/wiki/Riemann_sphere

I don't recall ever actually studying the Riemann sphere, which really seems to 
me like a gap in my education :-\



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