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Could any one tell me with an example, what is the relation between Order and Multiplicity of a holomorphic function on Riemann Surface,and how this formuale comes?

for example let $p\in X$ be not a pole for $f$, and $f(p)=z_0$ then $f(z)-z_o$ has a simple zero at $p$ so $mult_p(f-f(p))=1$,$ord_p(f-f(p))=ord_p(f)-ord_p(f(p))=1+0?$

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    The formula $ord_p(f-g)=ord_p(f)-ord_p(g)$ that you seem to use is false2012-07-25

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