*(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!"