Thanks,but you are...,Newton was not clear,...100 more years Cau

Don't worry, limit is funny, even for Newton....

The key point : your x=a^x is not right. a(n+1)=an^a(n-1), lim(an+1)=...=lim(an)^lim(a(n-1)),we have x=x^x,so,...an is variable not constant.

You may read Advance Calculus and then read Real Analysis.