A summary of my position so far.

I have indicated in previous posts that digits and symbols, as numbers, are not necessarily odd or even, finite or infinite, discrete or non-discrete, ordered or not ordered. Whether such descriptions are of properties which arise as a consequence of digits being expressed in particular applications (such as a sequence or calculus), or whether these are not properties but instead refer to stand-alone ontological elements I have not entirely determined. But logically it looks like the latter. For, regarding the former, we note that there is no substantive description of an element that is distinguishable from its properties; which would seem to rule this option out.

But I also reject the standard view that odd/even, finite/infinite, etc., refer to the ontologies of unique stand-alone numbers that are independent of the application in which they find themselves. What distinguishes this position from my own idea of a unique ontology of numbers is that in my view there is no universal framework in which all number ontologies and their applications must manifest. A consequence of my view is that numbers and digits are not transferable between applications. For example, the properties of numbers found in a sequence are not also of those found in a calculus; and, the digits of the discrete are not identical and freely interchangeable with the digits of the non-discreet (pi). Further, in my model digits or numbers are not transferable between applications. For example, the number 2 arises in a particular application - such as an application of an addition, and it is not interchangeable with 2 in another application of an addition.

Sets can be included in the list (first paragraph, top). That is, digits, as numbers, are not necessarily proportioned as a set, odd/even, etc. In the creation of a set, a plurality of elements yield a new element that also is neither necessarily odd or even, finite or infinite, etc. For example, a plurality of flowers is not itself a set as no new element is introduced as a set; but, a bouquet IS a set. It arises independently from a plurality of flowers as a new element. So created, and like the numbers, the set is also not necessarily odd or even, finite or infinite, etc. Also like the numbers, a set is not transferable between applications. For example, as a unique ontology, a set cannot be recast as an element in another set without also losing its unique ontological status as a set.
(c)
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Relevant Pages

  • Re: A summary of my position so far.
    ... Digits and symbols ARE NOT numbers. ... There is ZERO *necessity* of any particular symbol ... applications, so that is meaningless. ... number ontologies and their applications must manifest. ...
    (sci.logic)
  • Re: IEEE Decimal Float on Itanium
    ... Having it back in hardware might allow COBOL applications to see a performance increase. ... particular here requiring integer values larger than, say, quadwords?" ... gives us 31 digits) was adequated for the task. ...
    (comp.os.vms)
  • Re: Uniform point picking on a hexagon
    ... by truncating a random number you lose ... are introduced in the least significant digits. ... but for those applications in which information ... you might find completely artificial correlations. ...
    (sci.math.num-analysis)
  • Re: OT: Intel Macs - Official dual boot for XP
    ... All your applications will have large Help screens and six digits on hands and feet. ...
    (uk.rec.cars.modifications)