[FOM] Number theory proof mentioned by Frege
Rob Arthan
rda at lemma-one.com
Thu Apr 17 13:53:29 EDT 2008
On 16 Apr 2008, at 17:36, Chris Gray wrote:
> In "The Foundations of Arithmetic", Frege mentions a proof from
> pp.106-7
> of Hermann Henkel's Theorie der complexen Zahlensysteme.
>
> "Hankel proves that any closed field of complex numbers of higher order
> than the ordinary, if made subject to all the laws of addition and
> multiplication, contains a contradiction." Frege p. 106
>
> I have no copy of the Henkel book available to me. Is this a
> well-known
> result? Is this proof discussed or given elsewhere?
>
Conway and Smith's excellent "On Quaternions and Octonions" gives a
very accessible account of this and the generalisations when the laws
are relaxed to drop commutativity and then associativity.
Regards,
Rob.
More information about the FOM
mailing list