a degree of mobility of 0 i think technically would be no mobility... if one asks how much money you have and you say 0, you do not have a degree of money, you have no money, but that's just my opinion, i could be wrong...

right, and if you were out of a job and had 76 dollars in the bank( you have little wealth like regular infantry has little mobility) you would say I do not have wealth just like regular infantry would say they do not have mobility.
And I am not saying infantry could not move on there own, in WW2 there are many cases where infantry marched at amazing rates, it is just that they did not march at a rate such that the Militaries of the time thought they should be considered mobile.
Heinz Guderian was appointed Chief of
Mobile Forces in 1938, Mobile in this case meant all panzer, panzer grenadier and motorized divisions(which included halftracks(SdKfs251s) although I do not think any divisions at that time were labeled mechanized just panzer grenadier.
so we could go back to the roots of just what are we talking about to decide on the right name? Would it be better to try and classify two different types of Infantry units, or as upgrades, or based on national facts of what countries had, or an umbrella-unit that covers something beyond 'Infantry'? Germany had more horses in the Polish campaign than trucks to move materials and troops, so a couple units could be represented if more and more detail is desired...
thats an interesting idea, do you care to expand on that? i am just as interested in rules for logistics as new combat units