Re: Request for Peer Review - Refutation of Cantor Theorem Conclusion

Scott wrote:
Patricia:


I'm having trouble reading your notation. Could you give some examples?
What does each of the first few natural numbers each map to?


A function that maps N to 2^S, where P(S). Examples:

0 -> 00000000000000... = empty set
1 -> 10101010101010... = {0, 2, 4, 6, ...} = even numbers
2 -> 00000100000000... = {5}
3-> 01110101000101... = {1,2,3,5,7,11,13,...} = primes
...

Technically, I guess, there are an infinite number of such functions
depending upon the order of enumerating the powerset.

If I believed there were any order of enumerating the set of all strings
over {0,1} that includes all strings, finite and infinite, I would also
believe that N and P(N) have the same cardinality.

Can you prove the existence of even one such enumeration, let alone the
infinity you claim? Can you tell me a rule for finding where an
arbitrary string appears in your enumeration?

Of course, no matter what rule you tell me, I'll construct the string that differs in bit n from string n in your enumeration.

Patricia
.

Relevant Pages

  • Re: Well Ordering the Reals
    ... >> obviously the last of an unending set, which is the root of the contradiction. ... You mean the bit strings which are actually allowed to have infinite length, ... > countable bit string in my construction which maps to N, ... > Pdoes requiring something to map to *N means you have to ...
    (sci.math)
  • Re: md5 encryption
    ... >> Start with a given string, it will always map to the same hash. ... >> the hash, it could map to any one of an infinite number of strings. ...
    (alt.php)
  • Re: Oracle Connection Pooling
    ... > public String oracleFormatUrl(String prefix, String host, String port, ... > proprietaryException { ... > * Map from a resource attribute to a proprietary attribute. ... > protected void processCreateRequests ...
    (comp.lang.java.databases)
  • Re: Irregular review procedures for IACR sponsored conferences
    ... There are only three theorems. ... The second says that if you apply the map to an arbitrary but sufficiently ... long string, substrings of the image are uniformly distributed. ... the policy might look pretty dubious. ...
    (sci.crypt)
  • Google icosahedron problem the hard way
    ... mention of the "Google Labs Aptitude Test" and one of the ... the "Polya-Bernside Enumeration Theorem" which I didn't quite get. ... group elements instead of the subgroups. ... the entries in a table of 60*2^20 elements which map to themselves. ...
    (sci.math)