Hi all !

Yes, the J algebra is supposed to be a scientific paper product. Scientific papers of mathematics, logics and the J algebra defined in itself. It is supposed to exist before any implementation and to guide implementations. It is not supposed to include definitions which it would require infinite resources to compute, since we want to create an executable notation. This does not mean we could not handle infinity as a concept, as far as I understand. I don't understand the note about edge cases. There is a problem with most programs we write in that they can not handle all cases. We don't know for sure that they will always give correct results. That is a problem we want to address.

Erling Hellenäs

On 2017-08-09 09:47, Raul Miller wrote:
Your 2 prohibits your algebra from being completely implemented as a
programming language (since you have to support whatever you are going
to describe before you can use that in specifications, and because
computers have finite resources). So you are talking about a notation,
and not an implementation. But hypothetically speaking, you could use
J as a notation which is independent of any specific implementation.
(You presumably would want to specify whichever edge cases mattered to
you, when you do this.)

Generally speaking, though, mathematical logic deals with infinities
and other future equivalencies.


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