I've heard it is possible to prove, that some functions, for example defined with integral expressions, cannot be written with elementary functions (in somehow finite manner). Since I don't have a clue of how these things are proven, I'm now merely asking, that what kind of proofs these proofs are? What are they based on?(adsbygoogle = window.adsbygoogle || []).push({});

Since the problem setting seems similar to that of solving quintic, I must ask, does this thing have anything to do with Galois theory? I mean, could this be a reason to start studying it?

(I'm not sure wheter this belongs under analysis or algebra or logic or what...)

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# Impossible expressions

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