My intuition tells me that the proof of theorem 30.4 is incomplete. We can continue the pattern to infinity in theory, but because we never actually get to infinity we have no way of knowing down the line if the resulting decimal expansion is truly not achieved in our function... I am going to have to retrain my intuition.
I do not understand the proof that (0,1] has continuum cardinality. What is the purpose of S?
That was a short section...
-Batman
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