Im trying to find all satisfying valuations for an infinite set of formulas
$$M = \{A_1 \lor A_2, ¬A_2 \lor ¬A_3, A_3 \lor A_4, ¬A_4 \lor ¬A_5, A_5 \lor A_6, \dots\}$$ I cant really imagine myself solving this with my knowledge about sets in infinity so I would like to get a tip or two.
I'll assume this pattern continues, with $A_{2i-1} \vee A_{2i}$ and $\neg A_{2i} \vee \neg A_{2i+1}$ for all $i \ge 1$.
If any odd-numbered variable is false or any even-numbered one is true, then the sequence must alternate from that point on, with even-numbered variables true and odd ones false. On the other hand, if any odd-numbered variable is true or any even-numbered one is false, the sequence up to that point must alternate, with odd-numbered variables true and even-numbered ones false. So either the whole sequence is alternating $(F,T,F,\ldots)$ or $(T,F,T,\ldots)$, or there is one point where it switches: $(T,F,T,\ldots,F,F,T,F,T,\ldots)$ or $(T,F,T,\ldots,T,T,F,T,F,\ldots)$.