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Infinite tetration and superroot of infinitesimal
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.

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.


Messages In This Thread
RE: Infinite tetration and superroot of infinitesimal - by Ivars - 12/25/2007, 09:31 AM

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