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you don't need full AC, but at the very least countable.
We will now use [[proof by contradiction]] to show that the numbers in <math>[0,1]</math> are uncountable.
We will now use [[proof by contradiction]] to show that the numbers in <math>[0,1]</math> are uncountable.
Assume the numbers in [0,1], are countable. Then we can list them (without use of the [[Axiom of Choice]]) as such,
Assume the numbers in [0,1], are countable. Then we can list them (using only the countable [[Axiom of Choice]]) as such,
<math>
<math>