Russell's Paradox

[Rex]

A set has a god if you will, if we took all the sets in the world we would have a set of all sets.

Now if we had a set that are not members of themselves.

Then that set appears to be a member of itself if and only if it is not a member of itself.

Now that is a paradox.

I hope I got that right.

 

[Pah]

What is the set that is a member of itself - can you give an example? If you were to diagram it, woulf it be a set with a darker or more bold line around it.

I suppose it would be possible in a dimensional space greater that the customary four unless I'm missing something from set theory.

-pah-

 

[Rex]

Here you go

The paradox may be expressed in set theoretic terms. According to Cantor's set theory, a set is simply a collection of elements of some kind. The elements that a set contains may be other sets, and a set may even contain itself. For example, the set of mathematical ideas is itself a mathematical idea, so it contains itself. Russell considered a set X defined by the fact that X does not contain itself, and the set Y of all sets X.
Y={X: XÏX}
Russell then asked if Y contains itself. If it does, then since all sets contained in Y are sets that by definition do not contain themselves, Y cannot contain itself. If, on the other hand, Y does not contain itself, then it satisfies the definition for inclusion in Y, and so it does contain itself. If YÎY, then YÏY, which is a contradiction; but if YÏY, then YÎY, which is also a contradiction

 

[Pah]

Ahh yeah!

Douglas Hofstader once made a statement in Godel, Escher, Bach that many formal systems have no correspondance to reality. It is as true in Zeno's paradox as it is here.

I would say that the set of mathmatical ideas has no member that references itselt but is included in a mega set of two members which has a statement about the other member.A supra mega set could be shown that that makes a statement about this mega set and so on to infinity. I wonder if Godel's theory has application here - I would think so.

-pah-

 

[trishtrish10]

the near-east indians invented zero. math is sometimes illogical like its' Creator.