Prove that there are real numbers a1,a2,.. such that:
i) For all real numbers x, the serie f(x) \equal{} \sum_{n \equal{} 1}^\infty a_nx^n converge;
ii) f is a bijection of R to R;
iii) f'(x) >0;
iv) f(Q) = A, where Q is the set of rational numbers and A is the set of algebraic numbers. searchreal analysisreal analysis unsolvedBrazilian Undergrad MO