Myhill Theorem proof that the balanced braces language is not regular (idea)

Consider the words

w₁ = "(",
w₂ = "((",
...,
w_n = "("ⁿ,
...

(w_n is n open braces). Then, using the notation of the Myhill / Nerode theorem, S(w_n) is different for each n: it contains ")"ⁿ, but no other string of only close braces). Thus there are infinitely many types for S(w), so by the Myhill / Nerode Theorem the balanced braces language is not a regular language.