let $u$ be a smooth function such that $u|_{I_n}=1/n$. Let $\gamma=\{(s,u(s))\} \subset
\C^2$. Suppose $f$ is holomorphic on a neighborhood of the origin and that $f|_{\gamma}=0$, then $f(w_1,{{1} \over {n}})=0$ for all $n$ for $|w_1|$ small enough and thus $f \equiv 0$.

Background
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The first result on holomorphic extension of CR function is due to Lewy [@[Le]]. He proved that if a hypersurface was Levi nondegenerate at $p_0$ then CR functions extend holomorphically to one side of the hypersurface. This result was generalized by Boggess and Polking [@[Bo-Po]] for arbitrary dimensions. In the case of Levi flatness Trépreau [@[Tr-1]] proved that if a hypersurface in $\C^n$ is minimal at $p_0$ (it contains through $p_0$ no $n-1$ dimensional complex manifold), then CR functions extend holomorphically to one side of the hypersurface. The generalization of Trépreau’s result to arbitrary codimension is due to Tumanov [@[Tu-1]], in which he states that if the manifold $M$ is minimal at $p_0$ (it contains through $p_0$ no proper submanifolds of same CR dimension) then CR functions extend to a wedge in ${\C}^n$ with edge $M$. CR extension to manifolds of higher CR dimension has been dealt with in works by Taiani and Hill [@[Hi-Ta]], Tumanov 