Search results
In computational complexity theory and cryptography, an index set is a set for which there exists an algorithm I that can sample the set efficiently; e.g., on input 1 n, I can efficiently select a poly(n)-bit long element from the set.
17 kwi 2022 · Let \(\Lambda\) be a nonempty indexing set, let \(\mathcal{A} = \{A_{\alpha}\ |\ \alpha \in \Lambda\}\) be an indexed family of sets, and let \(B\) be a set. Use the results of Theorem 5.30 and Theorem 5.31 to prove each of the following: (a) \((\bigcup_{\alpha \in \Lambda}^{} A_{\alpha}) - B = \bigcup_{\alpha \in \Lambda}^{} (A_{\alpha} - B)\)
17 kwi 2020 · In short, saying that $I$ is an indexing set for $\mathcal A$ (or that $\mathcal A$ is indexed by $I$) is tantamount to giving a surjective (but sometimes it is implicitly assumed to be bijective) function $A_{(\bullet)}:I\to\mathcal A$.
Where the first entry in each pair is the index of each element (i.e., the element $(2,4)$ includes the information that the second element of the tuple is $4$). The set of all indices for such a tuple is called the index set, so in the above example the index is $\mathbb{Z}_{4} = \{1,2,3,4\}.$
8 lis 2019 · The set Λ is called the index and a is the indexed set. If I (λ) = a, then we write aλ for I (λ)." There's no examples and further explanations in the textbook. As far as I understood, Λ can be a set {1,2,3,4...} or, say {a,b,c,d..} and the set a can be {tree, fox, grass}.
10 paź 2024 · A set whose members index (label) members of another set. For example, in the set A= union _ (k in K)A_k, the set K is an index set of the set A.
Intersection and union can be performed on a group of similar sets identified by subscripts belonging to an index set. Consequently, intersection or union can be formed by naming a specific index set. A collection of sets can be a partition of a set if it satisfies two conditions.
