This is done by combining the compactness of the interval [0,1] (which implies that for any specific a∈\R we can always take a subsequence to make the sequence of numbers Fn(a) converge...This is done by combining the compactness of the interval [0,1] (which implies that for any specific a∈\R we can always take a subsequence to make the sequence of numbers Fn(a) converge to a limit) with a diagonal argument (for some enumeration r1,r2,r3,… of the rationals, first take a subsequence to force convergence at r1; then take a subsequence of that subsequence to force convergence at r2, etc.; now form a subsequence whose k-th term is the \(k\…