[om] DefMP elements

[Jacques Carette]

Bill Naylor <Bill.Naylor at mcs.vuw.ac.nz> wrote:
> Are these then the most general type of Numerical Value? 

A very general type of 'number' that mathematicians have come up with is Conway's set 'On' (to my knowledge, though I 
have researched this a lot).  There are isomorphic constructions from Model Theory as well.  And some similar 
constructions using Category Theory, but not quite as general(!).  It is a real closed field, but non-archimedean.  In 
a very precise sense, it is the biggest such.  It is interesting (to me) as it is possible to develop a very rich 
theory of analysis with On.

There are others who consider other generalizations (complex, quaternions, etc) to be numbers; I do not know where 
this 'stops'.  But since these have all very nice Matrix models, many have considered matricies to be generalized 
numbers as well. 

Trying to pin down 'the' definition of number is likely to be even more difficult than figuring out 'the' definition 
of sin.

Jacques
--
om at openmath.org  -  general discussion on OpenMath
Post public announcements to om-announce at openmath.org
Automatic list maintenance software at majordomo at openmath.org
Mail om-owner at openmath.org for assistance with any problems