kunen exercise about ccc which is not separable my question is about: show that if $\kappa > 2^\omega$, then the space $2^\kappa$ is not seperable. (kunen, page 86, exercise 4) –
ıf there exist a countable dense set $D$ where is the contradiction? since density of $D$ not clear for me in product space $2^\kappa$, I could not say anything about contradiction. 

Let's follow Carl's hint. If $D$ is a countable subset of $2^\kappa$, then we may enumerate $D=\{p_n\mid n\in\mathbb{N}\}$, and then associate to each $\alpha<\kappa$ the sequence $\langle p_n(\alpha)\mid n\in\mathbb{N}\rangle$, which is an element of $2^\omega$. Since $\kappa\gt 2^\omega$, it follows by the pigeon-hole principle that there must be two ordinals $\alpha\lt\beta$ giving rise to the same pattern, and thus $p(\alpha)=p(\beta)$ for all $p\in D$. From this, it follows that $D$ is not dense as Carl explains.
It is also interesting to note that the hypothesis $\kappa\gt 2^\omega$ is optimal, as $2^{2^\omega}$ is separable, a fact that is a consequence of David MacIver's answer to this MO question, using the Hewitt-Marczewski-Pondiczery theorem. 
