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Topic: Few questions on forcing, large cardinals
Replies: 17   Last Post: Mar 30, 2013 1:21 PM

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Posts: 1,968
Registered: 12/4/12
Re: Few questions on forcing, large cardinals
Posted: Mar 19, 2013 10:36 PM
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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.

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