Page:American Journal of Sociology Volume 5.djvu/414

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THE AMERICAN JOURNAL OF SOCIOLOGY

as the other can be considered the path corresponding to the continu- ation e f g h of 2/ the way open to w^ is, in fact, divided at e^ ^^e, into two branches. When z goes from d to /i through the branch-point e, then Wj, starting from d^ , can arrive at A, just as well as at h^ ; and the same is true of w^ starting from i^. In case the path of z leads through the branch-point, the final value of the function remains

/v

4

v^

^y.^

\

\

fc3

J

undetermined. If, on the contrary, z describe a path from 6 to h which does not pass through a branch-point, the final value of the function may differ according to the nature of the path, but it is for each definite path of z ahvays completely determined. A similar branching of the function takes place at those points at which w becomes infinite and therefore discontinuous. Thus, for instance, the

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point z = o is a branch-point both for the function w-

V'z

and for