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Hi Bob,
Thank you for your response, helped me a lot. I think I understand now with your example how the paradox works.
But I still have some questions if you don’t mind.
We have a library with books.
Then A librarian makes a series of catalogues of the books in the library.
You say he makes them, so I assume they are not part of the library.
Then my question is: Why should 'the catalogue of all books written in English', which is written in English contain itself? I don’t see the logic in this.
The catalogue of all books written in english says only something about the books in the library and nothing about itself.
Yes this catalogue may be a book and may be written in english but who cares, we were only making a catalogue of the books in the library.
More importantly, how do you know the librarian is a female?
I was reading a little bit about sets and of course Russell's paradox was mentioned.
From wiki: "According to naive set theory, any definable collection is a set. Let R be the set of all sets that are not members of themselves. If R is not a member of itself, then its definition dictates that it must contain itself, and if it contains itself, then it contradicts its own definition as the set of all sets that are not members of themselves. This contradiction is Russell's paradox. Symbolically:
"I do not exactly understand why we have to assume that there is a set R which is the set of all sets. Why do we have to assume that?
I mean, is it legal to start with something like this: "Let R be the biggest natural number. If R is ...".
Should be legal if you wanted to prove that there does (not)exists a biggest natural number but you can not say something about the natural numbers them selves.
Or is the russell paradox to show that such a set R does not exists? Thus that like natural numbers sets are in their own way infinite.
I have a feeling that I'm totally missing the point, so any help would be more than welcome.
btw sorry for my bad english, hope I made myself clear enough.
Hi,
Before last week the last time I opened my math books must be almost 15 years ago.
Then last week I opened a book and it reminded me how much fun math can be and how much I forgot.
So I decided to do a couple of hours a week some brain gymnastics.
I joined this forum in hope to have some help when something is not totally clear to me.
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