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Jan 28, 2010 at 14:10 comment added Joel David Hamkins Oh, I now see your comment C in your answer below, indicating that you may not welcome remarks about related ideas that other mathematicians believe to be important. In this case, please ignore my remark.
Jan 28, 2010 at 13:56 comment added Joel David Hamkins Your title would be better stated as: Is the addition of computable real numbers computable? The word decidable is usually applied to sets, when their characteristic function is computable, rather than functions. Your definable numbers are closely related to the concept of computable number used in the subject called computable analysis. In logic and model theory, the term definable number would mean it is the unique objects (in some structrue) satisfying some property expressible in a formal language. This notion often goes well beyond the computable.
Jan 27, 2010 at 20:33 answer added amaanush timeline score: -2
Jan 27, 2010 at 20:01 answer added François G. Dorais timeline score: 7
Jan 27, 2010 at 19:22 history asked amaanush CC BY-SA 2.5