Paradoxical Proof?

[BAndrew]

Technically there is no "smallest number" so if one number equals one word it is possible to go on infinitely long, right?

Actually there has to be a smallest natural number N (which we of course don't know).

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I read Berry paradox after reading the Russel's Paradox.

Here's the solution it proposes(from wikipedia)

The Berry paradox as formulated above arises because of systematic ambiguity in the word "definable". In other formulations of the Berry paradox, such as one that instead reads: "...not nameable in less..." the term "nameable" is also one that has this systematic ambiguity. Terms of this kind give rise to vicious circle fallacies. Other terms with this type of ambiguity are: satisfiable, true, false, function, property, class, relation, cardinal, and ordinal. To resolve one of these paradoxes means to pinpoint exactly where our use of language went wrong and to provide restrictions on the use of language which may avoid them.

This family of paradoxes can be resolved by incorporating stratifications of meaning in language. Terms with systematic ambiguity may be written with subscripts denoting that one level of meaning is considered a higher priority than another in their interpretation. "The number not nameable0 in less than eleven words" may be nameable1 in less than eleven words under this scheme.

Perhaps I am not smart enough, but I didn't understand the solution.