Schanuel's conjecture is that given any set of n complex numbers {z_i} which have linear independence over the rational numbers, the set (up to twice the size) has transcendence degree of at least n over the rationals. In mathematics, a set can be thought of as any well-defined collection of things considered as a whole. ... In mathematics, the complex numbers are an extension of the real numbers by the inclusion of the imaginary unit i, satisfying . ... In linear algebra, a family of vectors is linearly independent if none of them can be written as a linear combination of finitely many other vectors in the collection. ... In mathematics, a rational number (or informally fraction) is a ratio or quotient of two integers, usually written as the vulgar fraction a/b, where b is not zero. ... In abstract algebra, the transcendence degree of a field extension L/K is a certain rather coarse measure of the size of the extension. ...