It is also a name for the page and a half of indecipherable foreplay used in university physics textbooks before they give you the formula for something. Engineering student: I forgot the formula for the volume of a sphere, but I was able to figure it out from the area of a circle using calculus.
Bacterial is the taxonomy, i.e. the rank-based classification, of bacteria. In the scientific classification established by Carolus Linnaeus, each species has to be assigned to a genus (binary nomenclature), which in turn is a lower level of a hierarchy of ranks (family, suborder, order, subclass, class, division/phyla, kingdom and domain).
Proteobacteria are a major phylum of bacteria (over 32% of all known bacteria), have a great diversity and they are all Gram negative. Many are pathogenic (ie. Escherichia, Helicobacter, Salmonella). They are grouped into six classes: alpha (alphaproteobacteria), beta, delta, gamma, epsilon and zeta. Non-protobacteria are also Gram negative.