jaydfox Wrote:But omega IS qualitatively different. It is neither odd nor even. It is neither prime nor composite (though a statistical argument can be made that it's almost certainly composite). It IS greater than all natural numbers, by defintion. As such, if you want to relate 1/dx to existing models, the natural fit is omega. You could choose a larger (uncountable) infinity, but I don't see this as necessary, unless there is a strong reason to.
I was thinking of dx as a line segment, infinitesimal. A tangent to line x=x. Not a point. And not possible to create from finite number of points. As line segments that has direction but no magnitude. That are infinitely divisible but never You get a point as a result. So they are kind of extremely scalable . Would that qualify for omega?
Please see this- the only place I found so far something written what
I can also accept about infinitesimals. They in totality create a tangent space in all scales which exists, or can be assumed to exist.
http://publish.uwo.ca/~jbell/invitation%20to%20SIA.pdf
Although I do not think stopping at eliminating squares (nilsquared) is good enough-all infinite number of scales has to be involved simultaneously- therefore my interest in infinite tetration.
May be You can suggest other references (no points and sets, please), may be very old.
Ivars