Comments on: Set it Straight! http://yaniv.leviathanonline.com/blog/math/set-it-straight/ Strain your Brain Tue, 13 Sep 2011 13:21:47 -0700 hourly 1 http://wordpress.org/?v=3.1 By: Adib Ben Jebara http://yaniv.leviathanonline.com/blog/math/set-it-straight/comment-page-1/#comment-9762 Adib Ben Jebara Wed, 16 Jul 2008 03:59:06 +0000 http://yaniv.leviathanonline.com/blog/math/set-it-straight/#comment-9762 A mathematical why of the Big Bang Outline Let Ui be a set of locations of particles of the universe. U1xU2x ...... xUix ..... a set of infinite paths (Cartesian product). this set is equal to the void set by the negation of the axiom of choice. So there is no more space containing the particles. The particles collapse on themselves: Big Crunch. Then Big Bang. The Big Bang has taken place thus the negation of the axiom the choice is likely to considered as a good axiom. Adib Ben Jebara. A mathematical why of the Big Bang
Outline

Let Ui be a set of locations of particles of the universe.
U1xU2x …… xUix ….. a set of infinite paths
(Cartesian product).
this set is equal to the void set by the
negation of the axiom of choice.

So there is no more space containing the particles.
The particles collapse on themselves: Big Crunch.
Then Big Bang.

The Big Bang has taken place thus the negation of the axiom
the choice is likely to considered as a good axiom.
Adib Ben Jebara.

]]> By: yaniv http://yaniv.leviathanonline.com/blog/math/set-it-straight/comment-page-1/#comment-247 yaniv Wed, 31 Oct 2007 14:55:08 +0000 http://yaniv.leviathanonline.com/blog/math/set-it-straight/#comment-247 Hi Seb, I really like receiving comments like yours. Thanks! I will definitely write a post on the Banach-Tarski paradox and unmeasurable sets (whose existance depends on the axiom of choice ;-) ). In the meanwhile, have you seen: <a href="http://yaniv.leviathanonline.com/blog/riddles/spot-the-not/" rel="nofollow">Spot the Not</a>? It is not really related to the axiom of choice, but rather to unmeasurable sets. Hi Seb,

I really like receiving comments like yours. Thanks!

I will definitely write a post on the Banach-Tarski paradox and unmeasurable sets (whose existance depends on the axiom of choice ;-) ).

In the meanwhile, have you seen: Spot the Not?
It is not really related to the axiom of choice, but rather to unmeasurable sets.

]]> By: Seb Przd http://yaniv.leviathanonline.com/blog/math/set-it-straight/comment-page-1/#comment-246 Seb Przd Wed, 31 Oct 2007 14:24:18 +0000 http://yaniv.leviathanonline.com/blog/math/set-it-straight/#comment-246 Great post. Very interesting to see examples of theorems that you can prove or not without AC. I agree that Banach-Tarski is a great paradox, and would be very happy to see it here. Other topics that would be great: how AC is necessary to prove the existence of basis for vector spaces, how AC is related to Zorn's lemma and the well-ordering principle. I like the quote (from Wikipedia): "The Axiom of Choice is obviously true, the well-ordering principle obviously false, and who can tell about Zorn's lemma?" — Jerry Bona If you are into paradoxes and amazing results (I am) you could also tell us also about other undecidable or unprovable propositions (continuum hypothesis, Goodstein's sequence, the related Gentzen's theorem). The construction of unmeasurable sets is also very short and rather enlightening. Great post. Very interesting to see examples of theorems that you can prove or not without AC. I agree that Banach-Tarski is a great paradox, and would be very happy to see it here. Other topics that would be great: how AC is necessary to prove the existence of basis for vector spaces, how AC is related to Zorn’s lemma and the well-ordering principle. I like the quote (from Wikipedia): “The Axiom of Choice is obviously true, the well-ordering principle obviously false, and who can tell about Zorn’s lemma?” — Jerry Bona

If you are into paradoxes and amazing results (I am) you could also tell us also about other undecidable or unprovable propositions (continuum hypothesis, Goodstein’s sequence, the related Gentzen’s theorem). The construction of unmeasurable sets is also very short and rather enlightening.

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