Linear Independence/Dependence

by Gipson
Tags: linear
Mentor
P: 18,346
 Quote by Studiot I clearly defined the combination of elements and you clearly understood this. Why are you now asking for a zero set?
The book you quoted clearly talked about addition of two elements. So it makes sense that you would want to define A+B for A and B sets and that you want to have a zero set. If you cannot define these things, then your definition of "linear dependence of sets" is not compatible with the definition of Borowski.

 A vector is a set of points that satisfy certain conditions, specific to the problem in hand.
A vector is not a set of points. At least: nobody really thinks of a vector as a set of points. Depending on the set theory you choose, everything is a set. But I doubt many people in linear algebra see (a,b) actually as $\{\{a\},\{a,b\}\}$.

 Since this is getting further and further from the OP and personal to boot I withdraw from this thread.
That is perhaps the best decision.
Emeritus