## Example 7.3.5(b): Properties of Outer Measure

We have already proved this fact by elementary means (trying a diagonalized counting process and arriving at a contradiction). With the advanced machinery now at our disposal, the proof is only a single line.
If *[0, 1]* was countable, *m ^{*}([0, 1]) = 0*.
But

*m*, a contradiction.

^{*}([0, 1]) = 1 - 0 = 1