Comparing two notions of computable number
From: Axel Boldt (axelboldt_at_yahoo.com)
Date: 02/24/04
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Date: 24 Feb 2004 07:26:23 -0800
In http://wikipedia.org/wiki/Computable_number two notions of
computable number are given:
1) a real number a is computable iff there exists a Turing machine
which for given rational number eps produces a rational approximation
r such that |a-r|<eps
2) a real number a is computable iff there exists a Turing machine
which for given natural number n produces the n-th decimal digit of a
Definition 2 seems to be (equivalent to) Turing's original definition.
Clearly, every 2-computable number is 1-computable. Is the converse
also true?
Thanks,
Axel
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