Not quite clear exposition and definition. Need to be more exact.
In \hrefhttp://www.mathematics21.org/algebraic-general-topology.htmlmy book I defined (generalized) limit of any (e.g. non-continuous) function.
But applying it, to say, a differential equation (replacing the limit in the definition of derivative with my generalized limit) does not work because the components of the equation may be of different types (for example generalized limit of a function is not a real number).
To overcome this shortcoming I propose what I call meta-singular numbers.
[TODO: introduce the term singularity level above for a given number system.]
Let is a generalized limit. I will denote such number (or generalized limit of a lower rank) that where is a filter (that is is a limit of a constant function), if such exists. I will call reduced limit repeated applying to a generalized limit .
This definition is for now all I know about meta-singular numbers. It’s yet needed to formulate and prove some theorems.
See also \hrefhttp://www.mathematics21.org/binaries/reduced-limit.pdfthis rough draft on my site (in PDF format).
|Date of creation||2013-06-10 20:51:40|
|Last modified on||2013-06-10 20:51:40|
|Last modified by||porton (9363)|