Re: Objects and Relations

> One can use the Kuratowski pairs to present the order like a set of the pairs:
> { {{1}, {1, apple}}, {{2}, {2, orange}}, {{3}, {3, banana}} }

Below is a generalized version of the above expression. I have stripped away implied info that only exists in one's mind and not in the expression. What systematic method could a program take to determine the order of things? It should return the same result for the following two expressions as they are equivalent. How could it even begin to determine which things are being ordered, since set elements are unordered?

{ {{&}, {&, u8j}}, {{Mx7}, {Mx7, ^}}, {{-}, {-, 87nt}} } { {{&, u8j}, {&}}, {{-}, {-, 87nt}}, {{Mx7j}, {^, Mx7}} }

If one proposes that 1, 2, 3 ... are ordered, shouldn't they first [Quoted] [Quoted] show how to derived it from unordered sets? Received on Thu Feb 01 2007 - 02:54:47 CET