Do all known algorithms that generate infinitely many transcendental numbers like Gelfond-Schneider or Liouville only generate countably many? If uncountably many, is this set of measure zero?
Are known transcendental numbers countable?
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number-theory
elementary-set-theory
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2You shouldn't write "infinite transcental numbers" if you mean infinitely many transcendental numbers. "Infinite transcendtal numbers" means transcendental numbers each one of which, by itself, is infinite. Gelfond-Schneider doesn't generate any infinite numbers. – 2012-12-27
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1If a computer can generate the numbers (in some listed order), then it is countable. – 2012-12-27
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2Title needs fixing, all the known things are countable, transcendental or not. – 2012-12-27