Can anyone gove me a hint or a direction to the proof of this statement?
Let $F:V \rightarrow V$ be an operation, and $ \delta $ an ordinal. Prove, that there exists a unique function $g$ with domain $\delta$ such that, for every $ \alpha < \delta$, $g(\alpha)= F(\{g(\beta) ; \beta < \alpha\})$
An Operation, $F$ from $A$ to $B$ is a rule that, associates, for every $a \in A$ a unique $b \in B$. in a similar way to functions, we will say that $F$ is one to one if $F(a)=F(b) \Rightarrow a=b$ also $Im(F)=\{ f(A); A \in A \}$ and $F$ is onto $B$ if $Im(F) = B$
Thank you, Shir
Hint: Consider the least ordinal $\delta$ such that either there is no function with this property, or there is more than one function with this property.