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Nov 2, 2011 at 21:30 comment added Dejan Govc A similar example I find interesting is to take the unique positive solution of $x^x=x+1$. Then you can easily check that $x^{(x^{(x^x)})} =(x^x)^{(x^x)}$ using the defining equation and the usual exponentiation rules. Although the transcendentality doesn't seem obvious anymore ...
Oct 31, 2011 at 4:16 vote accept Vladimir Reshetnikov
Oct 29, 2011 at 3:01 history answered Todd Trimble CC BY-SA 3.0