Answer by José Carlos Santos for Need help with mathematical induction on...
Suppose that $a\mathop{R^n}b\implies a\mathop Rb$. Then, if $a\mathop{R^{n+1}}b$, there is a $c$ such that $a\mathop Rc$ and that $c\mathop{R^n}b$. But $c\mathop{R^n}b\implies c\mathop Rb$. So,...
View ArticleNeed help with mathematical induction on transitive relation problem.
Problem as follows:Let $R$ be a transitive relation. Let $aR^nb$ for $n \geqslant 1$, mean that there is a sequence of tuples: $$⟨a_0,a_1⟩,⟨a_1,a_2⟩, \ldots , ⟨a_{n-1},a_n⟩$$from $R$ such that $a_0 =...
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