Supposing that the definition of convexity that you're referring to is that of, for a set C with x_1 and x_2 being elements of C and for any scalar b between ze

Supposing that the definition of convexity that you're referring to is that of, for a set C with x_1 and x_2 being elements of C and for any scalar b between zero and one inclusively, [b * x_1 + (1 - b) * x_2] always being a member of C, I presume that you mean that errors, namely those kind of errors that are the subject of this thread's discussion, in mathematics will always symbolically be elements of some solution set of a finite number of linear equalities and inequalities (or the intersection of a finite number of halfspaces and hyperplanes).