On 5/8/2012 7:15 AM, Kevin Wampler wrote:
> On 5/8/2012 1:31 AM, Invisible wrote:
>>
>>> That's also why, even if complex cannot be extended in 3D, they can in
>>> 4D. (look at quaternion...)
>>
>> No. Quaternions do not form a field. Neither do the hypercomplex
>> numbers, nor any of the other 4D generalisations.
>>
>
> That's irreverent to Le_Forgeron's point. The application of the hairy
> ball theorem here does not depend on the numbers forming a field.

I should clarify, I took the fact that the extension wouldn't be a field 
to be implicit in Le_Forgeron's point, since the Hairy ball theorem's 
use doesn't depend on the numbers forming a field.  Not saying your 
reading was technically incorrect.

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