(7) A subset A of the real numbers is said to be dense if every open interval of the form (a,b) (where a

Extracted text: (7) A subset A of the real numbers is said to be dense if every open interval of the form (a,b) (where a < b)="" contains="" at="" least="" one="" point="" of="" a.="" for="" example,="" the="" rational="" numbers="" are="" a="" dense="" subset="" of="" the="" real="" numbers="" (so="" are="" the="" irrational="" numbers).="" let="" a="" be="" a="" dense="" subset="" of="" r.="" (a)="" prove="" that="" if="" f="" is="" continuous="" and="" f(x)="0" for="" all="" x="" e="" a,="" then="" f(x)="0" for="" all="" x="" e="" r.="" (b)="" prove="" that="" if="" f="" and="" g="" are="" continuous="" functions="" and="" f(x)="g(x)" for="" all="" x="" e="" a,="" then="" f(x)="g(x)" for="" all="" x="" e="" r.="" hint.="" use="" part="" (a).="" %3!="">