Prove that the set of recursive languages is infinite
The language {0}.
The language {00}.
The language {000}.
The language {0000}.
The language {00000}.
The language {000000}.
The language {0000000}.
The language {00000000}.
The language {000000000}.
The language {0000000000}.
The language {00000000000}.
The language {000000000000}.
The language {0000000000000}.
The language {00000000000000}.
The language {000000000000000}.
The language {0000000000000000}.
The language {00000000000000000}.
The language {000000000000000000}.
The language {0000000000000000000}.
The language {00000000000000000000}.
The language {000000000000000000000}.
The language {0000000000000000000000}.
The language {00000000000000000000000}.
The language {000000000000000000000000}.
The language {0000000000000000000000000}.
The language {00000000000000000000000000}.
The language {000000000000000000000000000}.
The language {0000000000000000000000000000}.
The language {00000000000000000000000000000}.
The language {000000000000000000000000000000}.
The language {0000000000000000000000000000000}.
The language {00000000000000000000000000000000}.
The language {000000000000000000000000000000000}.
The language {0000000000000000000000000000000000}.
The language {00000000000000000000000000000000000}.
The language {000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
The language {0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.
Which leads to the idea that we should consider the infinitely many languages of the form $\{0^n\}$ where $n \in \mathbb{N}$.