if I have a sequence $(x_n)_{n\geq0}$ such that $\lim_{n \to\infty } x_n = c$. Then why can I write: $\left | c-x_n \right | = \lim_{m \to\infty } \left | x_m - x_n \right |$
I tried to work it out but I get an inequality: $\left | c-x_n \right | \leqslant \left | c-x_m \right | + \left | x_m-x_n \right |$ Then as m tends to infinity the first term of the right side tends to zero. Is this the right way? What am I missing that makes both sides equal?
Thanks in advance.