效缥鼎 Non-Re languages Lemma:the set of all languages is uncountable Proof: fix an enumeration of all strings s,s2,S3,... (for example,lexicographic order) 0 a language L is described by its characteristic vector XL whose ith element is 0 ifs;is not in L and 1 ifs:is in LNon-RE Languages ◼ Lemma: the set of all languages is uncountable ◼ Proof:  fix an enumeration of all strings s1 , s2 , s3 , … (for example, lexicographic order)  a language L is described by its characteristic vector L whose ith element is 0 if si is not in L and 1 if si is in L