(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose X ⊂ R^n is a compact set, and U_1, U_2, U3, ... ⊂ R^n are open sets whose union contains X. Prove that for some n ∈ N (the natural numbers) we have X ⊂ U_1 ∪ ... ∪ U_n.

2. Relevant equations

A set is called compact if it is both closed and bounded.

3. The attempt at a solution

This problem seems trivial to me. If, as stated in the problem, U_1, U_2, U3, ... ⊂ R^n are open sets whose union contains X, does that mean that for some n we have X ⊂ U_1 ∪ ... ∪ U_n? I don't understand how there is anything to prove here. Any help would be appreciated.

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# Homework Help: Trivial set theory question?

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