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5. By using properties of outer measure, prove that the interval [0, 1] is not countable.

5. By using properties of outer measure, prove that the interval [0, 1] is not countable.

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Answer #1

Let is countable.

Then outer measure of is , because outer measure of countable set is .

We also know that outer measure of is .

So

This is contradiction our assumption so is uncountable.

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