Board index › Topical Discussion › Politics, Philosophy, and Religion

Zorn's Lemma

Page 1 of 1 [ 8 posts ] 

Previous topic | Next topic

Zornslemma
Raven
Raven

User avatar

Joined: 2 Jun 2009
Age: 45
Gender: Male
Posts: 104

04 Jun 2009, 12:04 am

Any partially ordered set such that every chain(totally ordered subset)has an upper bound, has a maximal element for the whole set itself. 8)



Saja
Raven
Raven

User avatar

Joined: 11 May 2009
Age: 59
Gender: Female
Posts: 112
Location: Netherlands

04 Jun 2009, 2:46 am

Love your username. I should have used AbelianGrape. That's my favorite joke ever (despite being one you can't tell much of anyone and expect laughter).


_________________
Much madness is divinest sense, to a discerning eye; much sense, the starkest madness. --Emily Dickinson
http://autism-fallingintoplace.blogspot.com


ruveyn
Veteran
Veteran

User avatar

Joined: 21 Sep 2008
Age: 89
Gender: Male
Posts: 31,502
Location: New Jersey

04 Jun 2009, 7:17 am

Zornslemma wrote:
Any partially ordered set such that every chain(totally ordered subset)has an upper bound, has a maximal element for the whole set itself. 8)


That is a very choice axiom.

ruveyn



DrizzleMan
Veteran
Veteran

User avatar

Joined: 30 Aug 2005
Age: 56
Gender: Male
Posts: 887

06 Jun 2009, 4:32 am

But the Banach Tarski paradox is obviously false.


_________________
The plural of platypus.


Zornslemma
Raven
Raven

User avatar

Joined: 2 Jun 2009
Age: 45
Gender: Male
Posts: 104

06 Jun 2009, 1:46 pm

DrizzleMan wrote:
But the Banach Tarski paradox is obviously false.


Oh really? Lets see some Proof! :wink:



DrizzleMan
Veteran
Veteran

User avatar

Joined: 30 Aug 2005
Age: 56
Gender: Male
Posts: 887

10 Jun 2009, 5:24 am

The full quote is, "The Axiom of Choice is obviously true, the well-ordering principle obviously false, and who can tell about Zorn's Lemma?" ;)


_________________
The plural of platypus.


twoshots
Veteran
Veteran

User avatar

Joined: 26 Nov 2007
Age: 40
Gender: Male
Posts: 3,731
Location: Boötes void

10 Jun 2009, 9:09 am

I've heard that quoted before; where does it come from?


_________________
* here for the nachos.


ruveyn
Veteran
Veteran

User avatar

Joined: 21 Sep 2008
Age: 89
Gender: Male
Posts: 31,502
Location: New Jersey

10 Jun 2009, 9:09 am

DrizzleMan wrote:
The full quote is, "The Axiom of Choice is obviously true, the well-ordering principle obviously false, and who can tell about Zorn's Lemma?" ;)


The well ordering principle is logically equivalent to the Axiom of Choice.

ruveyn