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

Prove that the interval [0,1] is not a zero set.

2. The attempt at a solution

Assume for contradiction that the interval [0,1] = Z is a zero set. This mean that given epsilon greater than 0, there is a countable coverage of Z by open intervals (ai, bi) (___I don't know what those intervals should be...___) such that the summation of bi - ai is less than epsilon.

But since Z is uncountable, there cannot be a countable coverable of Z by open intervals. Thus Z is not a zero set.

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# Homework Help: Real Analysis: Prove that the interval [0,1] is not a zero set

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