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I think this whole question is much better for a Wikipedia page. I don't think it's anywhere near over, especially as Sergeev probably doesn't disagree with the content of any of what has been said (with the tone yes, but not with the content), as he is not claiming a result in mathematical logic as far as I can see. There is nothing in what anyone has said here to prevent people (e.g. computer scientists) from using Grossone if they find it a simpler term to use, is there? "It's not even wrong- it's imprecise" Katz says; and Sergeev, I think, agrees, but sees this as a feature not a bug.
This answer refers to the expected volume of a tetrahedron with vertices chosen randomly in a unit volume tetrahedron, widely believed to be rational, until it turned out that it was in fact irrational.
