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In this talk,we investigate the number of regions of a real algebraic plane curve C defined by f(x,y)= 0 dividing the real plane R2.We obtain a relationship between the zero-th Betti number of R2\C and the number of bounded connected components of C,from which we derive a formula only involved with f(x,y)for the zero-th Betti number.It is a joint work with Mingbo Zhang.