Suppose that the function g : R -> R is continuous and that g(x) = 0 if x is rational. Prove that g(x)=0 for all x in R.
Follow Math Help Forum on Facebook and Google+
Originally Posted by wvlilgurl Suppose that the function g : R -> R is continuous and that g(x) = 0 if x is rational. Prove that g(x)=0 for all x in R. What is the epsilon-delta definition of "continuity"? What happens if you assume that g(x) is not equal to zero for some irrational number? Thank you!
View Tag Cloud