Example 7.3.5(b): Properties of Outer Measure

The set [0, 1] is not countable.
Context Context
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*([0, 1]) = 1 - 0 = 1, a contradiction.

Interactive Real Analysis, ver. 1.9.5
(c) 1994-2007, Bert G. Wachsmuth
Page last modified: Mar 28, 2007