The set of all polynomials with rational coefficients in dense in both spaces, the space of all continous functions defined in [a,b] C_([a,b]) with the metric(adsbygoogle = window.adsbygoogle || []).push({});

ρ(f,g)=max┬(1≤t≤n)〖|f(t)- g(t)|〗

( i hope you understand what i wrote ... prbl i will find a way to use mathml to write nicer ... :D )

Basically, if A is the set of all rational etc. , and C the countinous function space, the whole problem comes down to prooving A⊂[C], which implies to proove that the set of all polynomials has polynomial functions ( i.e. P[X] = f(x) ) which are continous ( from now on i use the metric from the space C, and that's it )

am i write ?

p.s.

i don't want a demonstration, becouse i want to learn how to do it myself

Thanks !!!!!!

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# A problem about dense sets

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