There are no legal numbers

This appears to establish that all integers* are illegal, via a less formal version the following argument.

*(and by a fairly obvious extension, all numbers)

• Some integers are illegal (in the sense, for example, that you can"t publish them without violating certain laws)
  
• Publishing encoded versions of illegal integers (say via some publicly available encoding algorithm) is also illegal
  
• Assume there is some smallest illegal integer, k
  
• It is presumably legal to publish k-1
  
• However, if I publish an algorithm to convert k-1 to an illegal integer (such as "add 1"), it would then be illegal to publish k-1, since with the algorithm it"s an encoded version of the illegal integer
  
• Hence, k-1 is an illegal integer
  
• Therefore, since the algorithm for converting one less than an illegal integer to an illegal integer has already been published, there is no smallest illegal integer
  
• A similar argument applies to any integer one larger than an illegal number (with the algorithm "subtract 1"), so there is no largest illegal integer.
  
• therefore, all integers are illegal.

"I"m sorry, I couldn"t do my arithmetic homework. It"s against the law!"