A subset S CR is called dense if for all a ER and all & >...

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A subset S CR is called dense if for all a ER and all & > 0 there exists x E S such that |x – a < 8. In formal notation, Va eR V8 > 0 x € S: x –- a| < 8. a) Prove that Q and IR – Q are both dense in R. b) Prove that if f: R → R is continuous, and fls = 0 for some dense subset SCR, then f = 0. A subset S CR is called dense if for all a ER and all & > 0 there exists x E S such that |x – a < 8. In formal notation, Va eR V8 > 0 x € S: x –- a| < 8. a) Prove that Q and IR – Q are both dense in R. b) Prove that if f: R → R is continuous, and fls = 0 for some dense subset SCR, then f = 0.