Dening the Tipping Point Based on Conditionally Convergent Series: Explaining the Indeterminacy

Tipping Point refers to the moment when an adaption or infection sustains itself in network without further ex- ternal inputs. Until now, studies have mainly focused on the occurrence of the Tipping Point and what it leads to rather than what precedes it. This paper explores the situation leading to the Tipping Point during a pro- cess of diffusion in networks. The core of the debate is to manifest that the process can be introduced as an example of conditionally convergent series and that de- termining the tipping points occurrence is conditional to the arrangement of the series based on Reimann Re- arrangement Theorem. Accordingly, the occurrence of curve does not follow a general formulation. That is called indeterminacy since that the predictions about tipping points for any diffusion over the network may include a variety of right answers, although such inde- terminacy neither means there is no tipping point nor many.