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[Hertz van Rental]

I would love it if you would point out the flaws that set theory has in it I'm taking that class right now.

Bertrand Russel wrote a whole treatise on it, and then wrote an addendum explaining why it was all wrong.
The problem with things like Set Theory is that they are a form of meta-language. It is a way of describing a system looking from the outside whilst the observer, and the language being used, are firmly rooted inside the system being described. In such a situation there will always be anomalies and contradictions.
For example, there must be a set of all sets, and if all sets are contained within this set then it must contain itself. This situation poses some interesting problems.
Or how about a set of all sets not contained within a set.
There are ways around these problems but it makes it a minefield.

You are right about non-Euclidian geometry, but it didn't really come into it's own until Einstein provided a need for it.

 

[monkeykoder]

Actually there cannot be a set of all sets there is no way to construct it. As for the set of all sets not contained within a set that statement makes no sense the actual "paradox" (it is known as Russel's paradox) is about the set of all sets that are not elements of themselves and to construct this set there would have to be a set of all sets which is not allowable in Zermelo Frankel set theory.

 

[Hertz van Rental]

Exactly. So there are sets which are impossible - showing that somewhere there is a flaw. If a theorem is sound then all cases fit within that theorem. If you find things that don't fit then the theory must be wrong somewhere.
And with set theory it is because it is a meta-language, and I have already explained the problem with those. This is why Barthes came unstuck in Linguistics - you can't use a system to describe itself.
I have to admit that I last looked at Set Theory and similar over 25 years ago - but as it didn't have much relevance to Photography I forgot most of it.
I think I might go back and re-read Russel (I named my cat after him )

 

[monkeykoder]

The set of all sets is a logical fallacy it SHOULDN'T be able to exist. As for the whole Meta Language thing I'm not exactly sure what you mean by the problems for it. The whole point of an axiomatic system is you have to make assumptions these assumptions are you're axioms and certain terms that cannot be defined readily like the term set in set theory. Something can only be called a set if it can be built with the language/axioms/theorems of set theory.