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22
votes
Are there any undecidability results that are not known to have a diagonal argument proof?
From a point of view your question relates to an "open conjecture" in computability theory.
I think you are asking if there is a specific problem $P$, which can be shown to be undecidable, but not wit …
50
votes
Two (probably) equal real numbers which are not proved to be equal?
One thing which I find crazy about this example (and which might ruin it for you), is that while this equation has never been rigorously proved, it’s truth/falsity is decidable by the decidability of real-closed …