query: Do all algabraic recursive functions have an equivalent non-recursive closed form function?
positive_passages.docid: 144772
positive_passages.text: Is there a recurrence relation which has no closed formula?
negative_passages.docid: 29647
negative_passages.text: Do there exist functions satisfying $f(x+y)=f(x)+f(y)$ that aren't linear?
negative_passages.docid: 122324
negative_passages.text: Is there a proof of Gödel's Incompleteness Theorem without self-referential statements?
negative_passages.docid: 42810
negative_passages.text: Is $(\mathbb{Q},+)$ isomorphic to $(\mathbb{Q}^n,+)$?
negative_passages.docid: 79067
negative_passages.text: Second level depth pure function?
negative_passages.docid: 70576
negative_passages.text: Elementary proof that $\mathbb{R}^n$ is not homeomorphic to $\mathbb{R}^m$
negative_passages.docid: 150719
negative_passages.text: All nonisomorphic trees of order $n$
negative_passages.docid: 55485
negative_passages.text: Recursive Function - $f(n)=f(an)+f(bn)+n$
negative_passages.docid: 38242
negative_passages.text: Explicit bijection between the successor of $\alpha$ and $\alpha$ (infinite ordinal).
negative_passages.docid: 77180
negative_passages.text: In pure functional languages, is there an algorithm to get the inverse function?
negative_passages.docid: 4800
negative_passages.text: Is there a name for an algebraic structure like this?
negative_passages.docid: 41363
negative_passages.text: when is f@g not the same as f[g]?
negative_passages.docid: 3902
negative_passages.text: Does $k+\aleph_0=\mathfrak{c}$ imply $k=\mathfrak{c}$ without the Axiom of Choice?
negative_passages.docid: 21202
negative_passages.text: Axiom of choice is equivalent to every relation includes a function with the same domain
negative_passages.docid: 4192
negative_passages.text: Non-algebraically closed field in which every polynomial of degree $<n$ has a root
negative_passages.docid: 85398
negative_passages.text: $\mathsf{ZF}$ is not finitely axiomatizable
negative_passages.docid: 135606
negative_passages.text: No function $f:\mathbb{Z}\rightarrow \{1, 2, 3\}$ satisfying $f(x)\ne f(y)$ for all integers $x,y$ and $|x-y|\in\{2, 3, 5\}$