3 problems

Let $(a_\alpha)$, $(b_\alpha)$, and $(c_\alpha)$ be the transfinite sequences of rational numbers, and let $\beta<\xi$. Suppose that $b_\beta=b/3^a$ with $\|b\|=3a+1$, and write…

Let $(a_\alpha)$, $(b_\alpha)$, and $(c_\alpha)$ be the transfinite sequences of rational numbers, and let $\beta<\xi$. Suppose that $a_\beta=b/3^a$ with $\|b\|=3a$, and write…

Let $(a_\alpha)_{\alpha<\xi}$, $(b_\alpha)_{\alpha<\xi}$, and $(c_\alpha)_{\alpha<\xi}$ be the transfinite sequences of rational numbers from the preceding conjecture. Denominator…