Infinite Pentation (and x-srt-x)

[tommy1729]

\( \eta < \text{srt}_{k+1}({k+1}) < \text{srt}_k(k) \) for all \( k \ge 5 \) by lemma (4) and lemma (5).
... In the limit, the squeeze theorem and completeness should guarantee that the limit exists and converges to \( \eta \).

Is this right?

I dont think so. When the sequence is decreasing and bounded it has a limit. But this limit could be probably bigger than \( \eta \). Or did I overlook something?

\( \eta < \text{srt}_{k+1}({k+1}) < \text{srt}_k(k) \) for all \( k \ge 5 \)

so the limit must be eta when lim k = oo because the rule is < and not =< , i think bo has overlooked that !?!

or did i miss something ?