There is x\in R such that 2=x^x^x^x^x^... Furthermore, I believe it should be possible to prove there is no field S such that R\in S, whereby 2=x^x^x^x^x^.... C

There is x\in R such that 2=x^x^x^x^x^... Furthermore, I believe it should be possible to prove there is no field S such that R\in S, whereby 2=x^x^x^x^x^.... Complex numbers don't help.