axiomatization of dependence
As noted by van der Waerden, it is possible to define the notion of dependence axiomatically in such a way that one can deal with linear dependence, algebraic dependence, and other sorts of dependence via a general theory. In this general theoretical framework, one can prove results about bases, dimension, and the like.
If is a subset of and , then .
If, for some set and some , it happens that but not , then .
If, for some sets and some , it happens that and, for every , it is the case that , then .
|Title||axiomatization of dependence|
|Date of creation||2013-03-22 16:27:46|
|Last modified on||2013-03-22 16:27:46|
|Last modified by||rspuzio (6075)|