On 3/19/2013 10:37 AM, JT wrote: > > No the infinity is not ***in the numbers*** there is infinity but it > ain't numerical. >
There are many number systems that are not related to natural numbers in the way you interpret the word: Complex numbers, Quaternion numbers, Octonian numbers, Icosian numbers, Miniquaternion numbers, Hurwitz numbers, etc.
What defines a number system abstractly is whether or not someone has constructed an arithmetic for the system of objects.
Infinity in the absolute sense is, of course, plural and not subject to arithmetical treatment as an object.
But, Cantor did develop an arithmetic that can be put in correspondence with the usual natural number arithmetic and extends to what are called transfinite numbers.
Because of deliberations on the opinions of people who feel as you do, I try to be careful. As much as possible, I use the term 'transfinite number' because that distinguishes from the sense of infinity that is necessarily plural.