query: Given two different sets, A and B, how many functions there are with domain A and codomain B?
positive_passages.docid: 55924
positive_passages.text: How many distinct functions can be defined from set A to B?
negative_passages.docid: 35362
negative_passages.text: Number of equivalence relations on a set
negative_passages.docid: 39090
negative_passages.text: Finding functions such that $f(g(x)) = f(x)g(x)$
negative_passages.docid: 90566
negative_passages.text: There exists surjections from A onto B and vice versa, and there is no bijection between the sets?
negative_passages.docid: 14711
negative_passages.text: set theoretic function, products of sets (product versus Cartesian product)
negative_passages.docid: 77735
negative_passages.text: When $\Bbb Z_n$ is a domain. Counterexample to $ab \equiv 0 \Rightarrow a\equiv 0$ or $b\equiv 0\pmod n$
negative_passages.docid: 137883
negative_passages.text: Cardinality of the set of all (real) discontinuous functions
negative_passages.docid: 155434
negative_passages.text: How is the codomain for a function defined?
negative_passages.docid: 46875
negative_passages.text: The identity morphism in $\mathbf{Set}$ is the identity function
negative_passages.docid: 40566
negative_passages.text: Counting surjective functions
negative_passages.docid: 124523
negative_passages.text: Finding an Inverse Function and Composition of Functions?
negative_passages.docid: 76826
negative_passages.text: Are there sets $A$ and $B$ such that $A \in B$ and $B \in A$?
negative_passages.docid: 140978
negative_passages.text: Real domain and range function to find all functions with nonzero x.
negative_passages.docid: 98363
negative_passages.text: Expanding two-variable function $f(x,y)$ over the complete sets $\{ g_{i}(x) \}$ and $\{ h_{j}(y) \}$
negative_passages.docid: 49592
negative_passages.text: Show that, if $f:A\to B$ is a function, with $A$ and $B$ being finite sets, and $|A|=|B|$, then $f$ is one to one iff $f$ is onto.
negative_passages.docid: 145785
negative_passages.text: Sets of functions closed within composition.
negative_passages.docid: 112566
negative_passages.text: Let $f,g$ be two distinct functions from $[0,1]$ to $(0, +\infty)$ such that $\int_{0}^{1} g = \int_{0}^{1} f $.