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Up: A non-r.e. language: Ld
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Suppose that some TM Mj accepts Ld. In that case, entry (j,j)
must be zero by definition of Ld. This means that wj is not in
L(Mj), which contradicts L(Mj)=Ld. Likewise, if entry (j,j)
is one, then wj is not in Ld, which contradicts L(Mj)=Ld.
Therefor, Ld is not r.e.