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Omni-MATH / Determine the number of sequences of sets S₁,S₂,…,S₉₉₉ such that S₁⊆S₂⊆⋯⊆S₉₉₉⊆{1,2,…,999} Here A⊆B means that all elements of A are also elements of B.

Problem

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problem

Determine the number of sequences of sets S1,S2,…,S999S_{1}, S_{2}, \ldots, S_{999} such that S1⊆S2⊆⋯⊆S999⊆{1,2,…,999}S_{1} \subseteq S_{2} \subseteq \cdots \subseteq S_{999} \subseteq\{1,2, \ldots, 999\} Here A⊆BA \subseteq B means that all elements of AA are also elements of BB.
Plain-text mathematical notation (without MathML)
Determine the number of sequences of sets S₁,S₂,…,S₉₉₉ such that S₁⊆S₂⊆⋯⊆S₉₉₉⊆{1,2,…,999} Here A⊆B means that all elements of A are also elements of B.
Original LaTeX notation
Determine the number of sequences of sets $S_{1}, S_{2}, \ldots, S_{999}$ such that $$S_{1} \subseteq S_{2} \subseteq \cdots \subseteq S_{999} \subseteq\{1,2, \ldots, 999\}$$ Here $A \subseteq B$ means that all elements of $A$ are also elements of $B$.

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Source and history

task_id
5026a297-bf2a-512e-99b6-d312ef9313aa
task_key
test--5026a297-bf2a-512e-99b6-d312ef9313aa
task_revision_id
1
config / split
/ test

Official source

initial import