MathDB

Suppose that

f:P(\mathbb N)\longrightarrow \mathbb N

and

A

is a subset of

\mathbb N

. We call

f

A

-predicting if the set

\{x\in \mathbb N|x\notin A, f(A\cup x)\neq x \}

is finite. Prove that there exists a function that for every subset

A

of natural numbers, it's

A

-predicting.
proposed by Sepehr Ghazi-Nezami

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