If yes, how? Also, I know you can't do it for arbitrary statements about real numbers, but that's not what I'm asking, and by "real" numbers, I mean the numbers constructible from 1, -, /, and the operations mentioned in the title.


Also, I don't care about numbers that can't be constructed from said operations and constant.



Is equality of terms for "real" numbers with roots, logarithm, exponential, sin, cos, and other trigonometric operations decidable with a Turing-machine?
Assuming [Schanuel's conjecture](http://en.wikipedia.org/wiki/Schanuel%27s_conjecture), the answer seems to be yes, according to Daniel Richardson, "How to recognize zero" *J. Symbolic Comput* **24** (1997), 627–645 ([doi:10.1006/jsco.1997.0157](http://dx.doi.org/10.1006/jsco.1997.0157), available [here online](http://people.bath.ac.uk/masdr/rec.ps)), in which the author defines a set of numbers he calls "elementary", which is algebraically closed and closed under exponential, logarithm and trigonometric functions, and for which equality is decidable (again, assuming Schanuel's conjecture).


