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 Yeah, my bet! a, b are real numbers I've constructed a linear function f: (0,1)->(0,2) defined by f(x)=2x such that f(1/2)=1, when x=1/2 (mid point of domain), y=1 (mid point of range) This linear function is certainly bijection, therefore |(0,1)|=|(0,2)| But how to prove |(0,1)|=|(a,b)| where a, b are real numbers and a