query: Can the empty set be the image of a function on $\mathbb{N}$?
positive_passages.docid: 152165
positive_passages.text: Why is there no function with a nonempty domain and an empty range?
negative_passages.docid: 58594
negative_passages.text: Is the empty set a subset of itself?
negative_passages.docid: 89205
negative_passages.text: Image under an entire function.
negative_passages.docid: 150825
negative_passages.text: Is an empty set equal to another empty set?
negative_passages.docid: 1307
negative_passages.text: Infimum and supremum of the empty set
negative_passages.docid: 117793
negative_passages.text: Finding a function $\mathbb{N} \to \mathbb{N}$ that is surjective but not injective.
negative_passages.docid: 44069
negative_passages.text: Proof that a continuous map to $S^n$ whose image is a proper subset of $S^n$ is null-homotopic
negative_passages.docid: 125502
negative_passages.text: Empty set literal?
negative_passages.docid: 121886
negative_passages.text: Proving image of $f:D^n\rightarrow \mathbb{R}^n \;$ contains $\;D^n$
negative_passages.docid: 113377
negative_passages.text: Empty preimage of an intersection implies empty intersection of the preimages
negative_passages.docid: 110669
negative_passages.text: Linear span of the empty set
negative_passages.docid: 143920
negative_passages.text: zeroes of non-zero holomorphic function form an atmost countable set
negative_passages.docid: 12402
negative_passages.text: Showing a function on $[0,1]$ is the zero function
negative_passages.docid: 107215
negative_passages.text: Is $\emptyset \in \emptyset$ or $\emptyset \subseteq \emptyset$?
negative_passages.docid: 88823
negative_passages.text: How can the empty set be open in the definition of the cofinite topology?
negative_passages.docid: 31212
negative_passages.text: The existence of the empty set is an axiom of ZFC or not?
negative_passages.docid: 62208
negative_passages.text: If $A$ is a non-empty set, then $A \notin A$