Proof of Sklansky's theorem?

[Ralle]

I've been reading Sklansky's book The Theory of Poker, and
found it to be a very good book indeed. Especially I find
the chapters on semi-bluffing and raising to be excellent.

But, there is one thing that is missing. On page 17-18 he
presents what he calls The Fundamental Theorem of Poker.
Intuitively this theorem appears to be correct, but since
it is called a theorem, a proof should be included, or at
least available. Does anyone know where a proof can be
found?

[SoBeDude]

Just because there is a theorem, doesn't mean a proof exists, or if it did, that would be easy to unnderstand. Have you even tried to decipher any but the most simplest proofs?

Look at the 4-color theorem thats what, a couple of centuries old? No true proof exists, but it was proven true by an exhaustive computer program within the last 5-10 years (can't remember the details).

So the 4-color theorem, which has been widely believed to be true for a very long time, was and still has never been proven by a traditional mathematics proof...although some of the world's best minds have tried.

So although he may (and I repeat MAY) be taking some literary license with the use of the word theorem, I believe the concept is very sound, and, just like the 4-color theorem, much computer simulation has proven the concept to be valid.

Just my thoughts!

-Scott

[Ralle]

> Just because there is a theorem, doesn't mean a proof exists

That is not correct. A theorem is something to which there is a proof.
Otherwise it is called conjecture, hypothesis or proposition.

> Have you even tried to decipher any but the most simplest proofs?

I have deciphered many proofs of different complexity.

[SoBeDude]

I have deciphered many proofs of different complexity.

So have I.

Show me the proof to the four color theorem.

-Scott

[Ralle]

I haven't seen the proof of the four color theorem. I don't
even know if it's a formal proof, or a computer search, though
I would imagine that it is a combination.

[SoBeDude]

As with Fermat's the four-color theorem is very old. No formal proof exists. It has been proven via computer however.

-Scott

[tdiddy]

Just because there is a theorem, doesn't mean a proof exists

Excuse me, but by definition a theorem is proposition that can be proved from accepted premises. So, actually if there is a theorem, there must also be a proof of a theorem. If there is no known proof of the proposition, then it is called a conjecture even if it is widely believed to be true. Of course, Fermat's Last Theorem was called a theorem before it was proven, but it was actually only a conjecture until it was recently proved true.

[SoBeDude]

yes, Fermat's last theorem is another example of a theorem without a proof...or at least it didn't have a proof for over 350 years.

I never saw it referred to as Fermat's last conjecture.

[Al Mirpuri]

Fermat's Last Theorem states that xn + yn = zn has no non-zero integer solutions for x, y and z when n > 2.

Concerning it, Fermat wrote "I have discovered a truly remarkable proof which this margin [Fermat is writing this remark in the margin of his copy of Diophantus's 'Arithmetica'] is too small to contain."

Fermat's proof was never found amongst his mathematical papers. Posterity labelled the Conjecture (because that is all it is without a proof) a Theorem because to do otherwise would have been to label Fermat a liar.

Andrew Wiles, the Princeton academic (an Englishman), who eventually solved it has expressed the fear that Fermat might well have had a simpler more beautiful proof that is now lost to history.

We will never know.

[M.B.E.]

Ralle is correct about what a "theorem" is.

"Fermat's last theorem" was something of a misnomer, and recognized as such in serious discussions. Some mathematicians did insist on labelling it "Fermat's conjecture".