NETMaths

Is this true?

A set of measure zero is countable

No — it is false.

The counterexample

The Cantor set

Uncountable, yet measure zero.

The kind of mistake this is

Hypothesis dropped

A theorem applied without checking one of its preconditions.

Drill statements like this

Others that fail the same way

From Lebesgue Measure and IntegrationMeasurable sets and functions

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