 This observation is really useful. For, it can be shown that when \(h_{i}\cdot b\cdot c^{n}\) is true and \(h_j\) is empirically distinct from \(h_i\), the continual pursuit of evidence is very likely to result in evidential outcomes \(e^n\) that (as n increases) yield values of likelihood ratios \(P[e^n \pmid h_{j}\cdot b\cdot c^{n}] / P[e^n \pmid h_{i}\cdot b\cdot c^{n}]\) that approach 0 as the amount of evidence increases. This result, called the Likelihood Ratio Convergence Theorem, will be investigated in more detail in  Section 4.  When that kind of convergence towards 0 for likelihood ratios occurs, the upper bound on the posterior probability ratio also approaches 0, driving the posterior probability of \(h_j\) to approach 0 as well, effectively refuting hypothesis \(h_j\). Thus, false competitors of a true hypothesis will effectively be eliminated by increasing evidence. As this happens, Equations  9*  through  11  show that the posterior probability \(P_{\alpha}[h_i \pmid b\cdot c^{n}\cdot e^{n}]\) of the true hypothesis \(h_i\) approaches 1. 