 comparing evidentially distinguishable alternative hypothesis \(h_j\) to \(h_i\) will very probably approach 0 as evidence accumulates (i.e., as n increases). Let’s call this result the Likelihood Ratio Convergence Theorem. When this theorem applies,  Equation \(9^*\)  shows that the posterior probability of a false competitor \(h_j\) will very probably approach 0 as evidence accumulates, regardless of the value of its prior probability \(P_{\alpha}[h_j \pmid b]\). As this happens to each of \(h_i\)’s false competitors,  Equations 10  and  11  say that the posterior probability of the true hypothesis, \(h_i\), will approach 1 as evidence  increases.[11]  Thus, Bayesian induction is at bottom a version of induction by elimination, where the elimination of alternatives comes by way of likelihood ratios approaching 0 as evidence accumulates. Thus, when the Likelihood Ratio Convergence Theorem applies, the Criterion of Adequacy for an Inductive Logic described at the beginning of this article will be satisfied: As evidence accumulates, the degree to which the collection of true evidence statements comes to support a hypothesis, as measured by the logic, should very probably come to indicate that false hypotheses are probably false and that true hypotheses are probably true. We will examine this Likelihood Ratio Convergence Theorem in  Section 4.[12] 