For future record,
this BW's ghost post comprises pseudo-math such as cardinality subtraction ("ℵ0−|{x}|=ℵ0"), wrong set-notation ("{ n^(1/k) | n,∀k∈N≠0 }"), wrong understanding of set-notation in the question, pretend expertise ("just a clarification for those mathematically inclined") and confounding remarks ("For those confused about the notation, n does not terminate in N.").