## Is the universe a tautology? (Explanation inside):

- 1. Is there a book in the library which describes the
**working**method of how to levitate and another which describes the same method of how to teleport? Or fly? Or gain super strength? Or whatever, the point is that it has to work in Real Life.

*How to build a computer?*book has one too. So my second question to discuss is:

- 2. Is the universe a tautology? If everything is possible and everything is not possible at the same time, what does this mean? Does anything exist at all?

**Malcolm Reynolds**

^{3}BestOf25th May 2011 02:07:45 AM from Finland , Relationship Status: Falling within your bell curve

edited 25th May '11 2:08:00 AM by BestOf

^{5}BestOf25th May 2011 02:29:59 AM from Finland , Relationship Status: Falling within your bell curve

edited 25th May '11 2:37:32 AM by Carciofus

**the working methods**of how to break the laws of nature. Am I wrong?

edited 25th May '11 3:03:21 AM by Sati1984

**Malcolm Reynolds**

**Malcolm Reynolds**

**Malcolm Reynolds**

__*__

__*__It's the same thing as saying that the Library will not contain a number which is even and odd. The fact that the library is infinite, or that it contains all combinations of characters, is irrelevant here: the Library will not contain this number, because all odd numbers are not even and all even numbers are not odd.

edited 25th May '11 3:35:24 AM by Carciofus

**ALL**the stars!

edited 25th May '11 4:25:35 AM by Yej

edited 25th May '11 4:29:04 AM by Carciofus

**ALL**the stars!

**R**| books?

__*__I'm fairly sure that even the set of all possible strings of all possible alphabets is still only |

**Z**|.

edited 25th May '11 4:33:08 AM by Yej

**R**| books, but why stop here? If you want to go even higher in the transfinite hierarchy, you treat each one of these books as if they were page numbers instead of books: that is, you develop another kind of "book" which is a display that lets you enter one of the first-level "books" and return the corresponding page. In a certain sense that can be made precise, there are more "second level books" of this sort than there are "first level books". Then you repeat the procedure again, and build "third level books", "fourth level books", and so on. You do this for for all integer levels. Then what can you do? Why, of course, you can build "omega-th level books" that take in input

*any*book of a previous level and return a page. Then you build "omega-plus-one-th" level books, "omega-plus-two-th" ones, and so on, up to infinity. And then you do it again, and again, and again, and do this too infinitely many many times, and then you do

*this*infinitely many times, and so on. Again, the practical details are left to the reader - what am I, an engineer? Transfinite arithmetics is freaky.

edited 25th May '11 4:53:07 AM by Carciofus

**ALL**the stars!

*is*reducible to a real number, though. So the second-level books are basically books with a real number of pages. And there are more books of this sort than there are real numbers, by Cantor's Theorem.

edited 25th May '11 4:50:22 AM by Carciofus

**ALL**the stars!

*is*freaky.

edited 25th May '11 4:54:44 AM by Yej

edited 25th May '11 5:02:24 AM by Carciofus

**Malcolm Reynolds**

edited 25th May '11 5:05:52 AM by Carciofus

**ALL**the stars!

- Any finite alphabet A is going to be isomorphic to a subset of the natural numbers, specifically {0,1,2,..|A|}.
- Start with a "blank" book composed entirely of 0s, and imagine this book written right-to-left.
- Interpret the text of the book as a natural number in base |A|.
- The text of the next book is defined as adding one to this number.
- This procedure will, eventually, produce every possible book.
- Thus, the books are enumerable.
- Thus, the set of all books is isomorphic to |Z|.

edited 25th May '11 5:07:18 AM by Yej

- This procedure will, eventually, produce every possible book.

Book 1: BAAAAAA....

Book 2: ABAAAAA....

Book 3: BBAAAAA...

Book 4: AABAAAA... and so on. All the books of your list end with a trailing sequence of AAAAA, and therefore the book BBBBBB... will not be in your list. More in general, for any listing as the above one I can pull a Cantor and write another book which is different from Book 0 in the first character, from Book 1 in the second one, and so on. For the one you gave me, it would be the book BBBBB...., but ABABABABAB.... would also work as a counterexample for that case. The important thing here is that for

*any*listing that you could give me, Cantor's method gives me a counterexample.

edited 25th May '11 5:25:08 AM by Carciofus

**ALL**the stars!

*start*with BBB... and CCC... and combine all the results? ) Now what are you going to do with your real-numbered books?

edited 25th May '11 5:26:44 AM by Yej

edited 25th May '11 5:35:36 AM by Carciofus