Re: Objects and Relations
From: NENASHI, Tegiri <tnmail42_at_gmail.com>
Date: Wed, 31 Jan 2007 21:15:43 +0100 (CET)
Message-ID: <Xns98C99B8FCFFDAasdgba_at_194.177.96.26>
>
> The above two statements are contradictory. First you say set elements
> have no order. Then you say a second set whose elements are also
> unordered imply the order of the elements of the first set. But this
> is contradictory as we already established in the beginning that the
> elements of the first or any set are unordered.
>
> Let me try to apply your "system":
>
> I am assuming { {1, apple}, {2, orange}, {3, banana} } would imply the
> order
Date: Wed, 31 Jan 2007 21:15:43 +0100 (CET)
Message-ID: <Xns98C99B8FCFFDAasdgba_at_194.177.96.26>
"Neo" <neo55592_at_hotmail.com> wrote in news:1170271418.255398.256830_at_p10g2000cwp.googlegroups.com:
>> > I still can't understand the logic/rationale explaining the >> > transition from sets with unordered elements to sets with ordered >> > elements, either from above or Chapter 7 of Schuam's Outline. >> >> Hint: there *are no* sets with ordered elements. There are sets >> of unordered elements, and there are *other* sets of unordered >> elements that contain information that specifies an order for another >> set.
>
> The above two statements are contradictory. First you say set elements
> have no order. Then you say a second set whose elements are also
> unordered imply the order of the elements of the first set. But this
> is contradictory as we already established in the beginning that the
> elements of the first or any set are unordered.
>
> Let me try to apply your "system":
>
> I am assuming { {1, apple}, {2, orange}, {3, banana} } would imply the
> order
No, it would not imply the order. 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}} }
i.e { (1, apple), (2, orange), (3, banana) }
>
> And if { {1, 100}, {2, 34}, {3, 200} } implies the order 100, 34 and
> then 200. The would the following should imply the same: { {34, 2},
> {3, 200}, {1, 100} }
{ {1, 100), (2, 34), (3, 200) } where (a, b) def.= { {a}, {a, b} }
>
>
Received on Wed Jan 31 2007 - 21:15:43 CET