Gödel's completeness theorem

[chrisheaven]

Gödel's completeness theorem says that a deductive system of first-order predicate calculus is "complete" in the sense that no additional inference rules are required to prove all the logically valid formulas. A converse to completeness is soundness, the fact that only logically valid formulas are provable in the deductive system. Together with soundness (whose verification is easy), this theorem implies that a formula is logically valid if and only if it is the conclusion of a formal deduction.

 

[milagros317]

You're back to mathematical logic again. 😱

 

[chrisheaven]

what??? NO trainwreck??

 

[chrisheaven]

Der Gödelsche Vollständigkeitssatz (benannt nach Kurt Gödel) ist der Hauptsatz der mathematischen Logik. Er zeigt für das Hilbert-Kalkül (ein formales System der Prädikatenlogik erster Stufe) die Korrektheit und Vollständigkeit: Jeder Satz, der semantisch aus einer Formelmenge folgt, lässt sich mit den Schlussregeln des Systems aus der Formelmenge herleiten, und umgekehrt. Für die Logik erster Stufe sind also syntaktische und semantische Folgerung gleichbedeutend.

 

[milagros317]

what??? NO trainwreck??

I will give your mathematical threads a rating of neutral, zero train wrecks. 😀

 

[chrisheaven]

excellent

 

[Bohemianne]

 

[chrisheaven]

That is a graph of a sliding derivative line.
Interesting nevertheless

 

[Bohemianne]

^ I don't know if it is interesting enough, but at least the slope and animation is silly.

 

[chrisheaven]

very true----- I fear you must have found it by watching the following video clip.!!
http://www.dailymotion.com/gb/relevance/search/bullshit/5#video=xf3nnr

 

[milagros317]

Very cute. 😀

 

[Bohemianne]

Very cute. 😀

Thanks, Mils! Somehow Math has its own tight-slope-walkers...

 

[chrisheaven]

Very cute. 😀

Mils, I am uncertain as to how this is connected with the title of the thread!

 

[Bohemianne]

Mils, I am uncertain as to how this is connected with the title of the thread!

...carthesian plane + cute factor.

 

[milagros317]

Mils, I am uncertain as to how this is connected with the title of the thread!

It isn't. 😛

 

[chrisheaven]

I suspected as much-- but was as usual far too polite to point it out

 

[Bohemianne]

^ Uh... how about this?

 

[chrisheaven]

rather simplistic, I feel

 

[milagros317]

How about Maxwell's Equations? 😀

 

[chrisheaven]

better!

 

[chrisheaven]

Maxwell's equations represent one of the most elegant and concise ways to state the fundamentals of electricity and magnetism. From them one can develop most of the working relationships in the field. Because of their concise statement, they embody a high level of mathematical sophistication and are therefore not generally introduced in an introductory treatment of the subject, except perhaps as summary relationships.

These basic equations of electricity and magnetism can be used as a starting point for advanced courses, but are usually first encountered as unifying equations after the study of electrical and magnetic phenomena

 

[milagros317]

I'm glad you liked it. 😀

 

[chrisheaven]

I actually did!

 

[milagros317]

I actually did!

IMO, James Clerk Maxwell is underrated. He should be up there with Newton in reputation. 😀

 

[chrisheaven]

Here he is as a YOUNG man