Re: What if Carl Friedrich Gauss was wrong?

On 03/01/2025 07:58 AM, Python wrote:

Le 01/03/2025 à 16:57, Ross Finlayson a écrit :

On 03/01/2025 07:43 AM, Ross Finlayson wrote:

On 03/01/2025 06:52 AM, Python wrote:

Le 01/03/2025 à 03:29, Ross Finlayson a écrit :

[snip nonsense]

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Of course many people are familiar with the theorem that
the complex numbers are a complete ordered field and so
are the real numbers and that's unique up to isomorphism,
yet for example I wrote field operations equipping [-1, 1]
with field operations, another, different, complete ordered
field.

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Complex numbers form a complete field but NOT an ordered field.
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Yeah, now that you mention it, an ordering would
be a bit contrived, ....
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It's usually enough called "Gaussian screw arithmetic"
or "Wick rotation".

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Hmm... Not quite. This is just name dropping.
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Also there's another one on [-1, 1].

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Interesting? Which is?

I wrote it in a reply to Virgil about
"the linearity WM failed to find", or
something like that, basically by taking
the limit of some functions the hyperbolic.
Fifteen or twenty years ago, ....