2 replies to this topic

[knite]

I was just reading a book on elementary calculus I got for free from the internet, <3 internet, and was learning it from the book, and though Im not very far into it, I did just read about infinitesmals(which I read is contrary to how most people learn, but thats how this one teaches.) and I was wondering, if an infinitesmal is translated from hyperreal to real, wouldnt a number that renders lights motion in "change of time" smaller than the length of a string in string theory be enough to give absolutely precise data without being forced to use "kind of real" numbers?

[chubtoad]

The infinitesimal approach to analysis (calculus) is generally known as nonstandard analysis. Its a little strange when you first here about it (every real number has this halo of infinitely close numbers around it) but apparently it has made the proofs of many theorems shorter and more enlightening. Basically nonstandard analysis is the formalization of the kind of calculus mathematicians like Newton and Gauss did. If you read one of Gauss's proofs it will start out normally and then he will say something crazy like "let u be an infinite number" and proceed to do operations on it and get a result people later proved is true with standard analysis. It will be interesting to see if the nonstandard approach can take over the standard approach in the years to come.

[knite]

I was just wondering, if cE= < P, where c is the speed of light, and P is the Planck length, then E must be the time in which light travels a distance that is less than or equal to the Planck length, a length which, when less than, has no meaning, with this, you could use a finite number to replace the infinitesmal, could you not?

Edited by knite, 02 July 2005 - 11:07 PM.