query: Number of functions from $A$ to $A$
positive_passages.docid: 145873
positive_passages.text: Let $X$ and $Y$ be finite sets. Then the set $Y^X$ is finite and $\#(Y^X) = (\#Y)^{\#X}$.
negative_passages.docid: 7938
negative_passages.text: Number of Homomorphisms from $\Bbb{Z}_m$ to $\Bbb{Z}_n$
negative_passages.docid: 146055
negative_passages.text: Proving a set of functions is uncountable
negative_passages.docid: 24810
negative_passages.text: Functions satisfying $(b-a)f'(\tfrac{a+b}{2}) = f(b)- f(a)$
negative_passages.docid: 38260
negative_passages.text: How many functions are possible to create in this example?
negative_passages.docid: 146436
negative_passages.text: Cardinality of the set of bijective functions on $\mathbb{N}$?
negative_passages.docid: 6632
negative_passages.text: Sequence of differentiable functions
negative_passages.docid: 27865
negative_passages.text: What is the number of invertible $n\times n$ matrices in $\operatorname{GL}_n(F)$?
negative_passages.docid: 74829
negative_passages.text: Number of non decreasing sequences of length $M$
negative_passages.docid: 9971
negative_passages.text: enumerative combinatorics,In how many ways (as a function of n) can one choose a composition α α of n
negative_passages.docid: 42794
negative_passages.text: Prove that functions map countable sets to countable sets
negative_passages.docid: 4310
negative_passages.text: Range of $(a_{1}-a_{2})^2+(a_{2}-a_{3})^2+(a_{3}-a_{4})^2+(a_{4}-a_{1})^2$ is
negative_passages.docid: 26169
negative_passages.text: Function $f: \mathbb{R} \to \mathbb{R}$ that takes each value in $\mathbb{R}$ three times
negative_passages.docid: 13273
negative_passages.text: Cardinality of the set of all real functions of real variable
negative_passages.docid: 409
negative_passages.text: functions satisfying $f(x - y) = f(x) f(y) - f(a - x) f(a + y)$ and $f(0)=1$
negative_passages.docid: 55924
negative_passages.text: How many distinct functions can be defined from set A to B?
negative_passages.docid: 112049
negative_passages.text: How many elements does $\mathcal{P}(A)$ have?