效绵鼎 Proof-Continued Clearly,L is a language over {0,1}. Thus,it is the j-th anguage for som X particular j. Recall:L={ww is the Let x be the j-th string i-th binary string and wis not in the i-th language). Is x in L? If so,x is not in L by definition of L. j-th If not,then x is in L by definition of L. .1414 Proof – Continued ▪ Clearly, L is a language over {0,1}. ▪ Thus, it is the j-th language for some particular j. ▪ Let x be the j-th string. ▪ Is x in L? ▪ If so, x is not in L by definition of L. ▪ If not, then x is in L by definition of L. Recall: L = { w | w is the i-th binary string and w is not in the i-th language}. x j-th Lj