These redundancies can be avoided by considering only pairs ("n","m") such that "n" > 0 and "m" ≥ 0; that is, where the direction of the vector w lies between those of u (inclusive) and v (exclusive). It can be verified that every nanotube has exactly one pair ("n","m") that satisfies those conditions, which is called the tube's type. Conversely, for every type there is a hypothetical nanotube. In fact, two nanotubes have the same type if and only if one can be conceptually rotated and translated so as to match the other exactly.