What are your Fav Theorems.

[myrkle]

Fermat's Last Theroem

 

It says that if you replace the exponents in the Pythagorean theroem to any interger greater than 2 there will be no answer, but this was proven wrong over 300 years later by Andrew Wiles. Even if it was right it would be useless

[haggy]

You obviously don't know much about Fermat's Last Theorem.

[zaphod]

You obviously don't know much about Fermat's Last Theorem.

 

:thumbsup:

[matt grime]

Euclids parallel postulate is an axiom and not a theorem.

 

I would say Riesz's Representation theorem : The dual of every hilbert space can be isometrically isomophically embedded into itself.

 

Mandrake

 

You might change your mind if you saw the full banach space version of that.

[matt grime]

In terms of "really, wow, who'd've thought that":

 

All automorphisms of S_n are inner unless n=6. (Why 6, is what should spring to mind).

That Dynkin diagrams not only parametrize (simple) Lie algebras, but things about representation types of quivers too. If anyone wants the full explanation let me know.

That the outer automorphism just a few lines back is how (some?) of the exceptional simple groups arise.

 

 

Important ones:

Did someone mention Bolzano Weierstrass? That every sequence lying in a closed bounded subset of R^n has a convergent subsequence.

Fundamental theorem of Calculus. F(x)= int_0^x f(t)dt => F' = f (assuming f continuous) and its variations.

[Dave]

At the moment I'm loving te Weierstrass M-test:

 

Let [math]f : A \to \mathbb{R}[/math] with [math]A \subset \mathbb{R}[/math]. Suppose there exist [math]M_n[/math] with [math]|f(n)| \leq M_n[/math] with [math]\sum_{n=1}^{\infty} M_n[/math] convergent. Then we have that [math]\sum_{n=1}^{\infty} f(n)[/math] converges uniformly on A.

 

Absolutely great

[zaphod]

stupid series

[bloodhound]

At the moment I'm loving te Weierstrass M-test:

 

w00t we just finished doing that as well. its quite cool result

 

just doing step functions and reimann integrals now.