query: Function and its inverse in Discrete Mathematics
positive_passages.docid: 17212
positive_passages.text: The preimage of a subset
negative_passages.docid: 127069
negative_passages.text: Discrete Math - Counting
negative_passages.docid: 125174
negative_passages.text: Combinatorial intuition of identity
negative_passages.docid: 10850
negative_passages.text: Are all functions that have an inverse bijective functions?
negative_passages.docid: 91545
negative_passages.text: A stronger version of discrete "Liouville's theorem"
negative_passages.docid: 146436
negative_passages.text: Cardinality of the set of bijective functions on $\mathbb{N}$?
negative_passages.docid: 5448
negative_passages.text: Finding the closure of some subsets of the ordered square
negative_passages.docid: 154240
negative_passages.text: Inverse of Heine–Cantor theorem
negative_passages.docid: 25553
negative_passages.text: elementary set theory (cartesian product and symmetric difference proof)
negative_passages.docid: 70327
negative_passages.text: the numer of partial function between two sets in combinatoric way
negative_passages.docid: 114277
negative_passages.text: Proving in Discrete Structures Problem that $2^N = \binom{N}{0} + \binom{N}{1} + \binom{N}{2} + \dots + \binom{N}{N}$
negative_passages.docid: 52040
negative_passages.text: "Inverse" of an $n\times k$ matrix.
negative_passages.docid: 157765
negative_passages.text: What would a Cayley table of inverse semigroup look like?
negative_passages.docid: 13193
negative_passages.text: Does a inverse function need to be either surjective or injective?
negative_passages.docid: 74453
negative_passages.text: Injective and Surjective Functions
negative_passages.docid: 10024
negative_passages.text: How to prove $(f \circ\ g) ^{-1} = g^{-1} \circ\ f^{-1}$? (inverse of composition)
negative_passages.docid: 101313
negative_passages.text: Minimal polynomial, determinants and invertibility