On 3/11/2014 3:23 PM, John Gabriel wrote: > On Tuesday, 11 March 2014 21:46:21 UTC+2, Martin Shobe wrote: > > >> That's what I said. What you've failed to realize is that this is true >> for every magnitude. So every magnitude is a multiple of a unit and >> therefore not incommensurable. > > You are very confused, but that does not surprise me in the least. :-) > > No, if a magnitude is a multiple of a unit, then it is very much commensurable. If a magnitude can be expressed in any combination of units or parts of units, then it is commensurable. > > If a magnitude cannot be expressed in any combination of units or parts of units, then it is incommensurable. > > Quite simple. You just don't get it! :-) >
I get it. I even get what you are trying (and failing) to do. I used all of that to arrive at my conclusion. By your construction, there are no incommensurable magnitudes since any magnitude (AB) is a multiple of the unit AB : AB.