Hi--

Where can i find a proof of this theorem: For each $r \in \mathbb{Z}_{+}$, there exists a Complex entire function $f(z)$ such that $f(r) \neq 0$ but  $f(r+1)=f(r+2)=\cdots =0$, i.e $f(z) \in I_{r+1}$ but $f(z) \neq I_{r}$, where  $I_{r}= \{ f \in R \ | f(r)=f(r+1)= \cdots =0\}$ where $R$ is the ring of complex entire functions

Hi--

Where can I find a proof of this theorem: For each $r \in \mathbb{Z}_{+}$, there exists a complex entire function $f(z)$ such that $f(r) \neq 0$ but  $f(r+1)=f(r+2)=\cdots =0$, i.e. $f(z) \in I_{r+1}$ but $f(z) \neq I_{r}$, where  $I_{r}= \{ f \in R \ | f(r)=f(r+1)= \cdots =0\}$ where $R$ is the ring of complex entire functions