A word cannot be described within the same language
Here's a proof that any word in a language cannot be described within the same language.
Proof by Induction #
Assume that each word takes at least one other word to define. Also assume that circular definition is not allowed. And finally, assume that a language can be constructed by adding word one by one.
Basis: Suppose a language consists of one word. Then trivially, this word cannot be described in terms of other words in the language. Thus the word cannot be described.
Inductive step:
Suppose the statement is true for
Hence basis and inductive steps have been proven. By mathematical induction, the statement is true. Q.E.D.