One general and natural technique in mathematics is to approximate any system via linear systems. These linear systems are especially vector spaces or normed spaces.
Matrices are used for repesenting linear transformations between these spaces. I.e, A matrix is a function between two...
Definable sets and in particular definable numbers is one of the topic in Model Theory .
Please see the definition of the terms "A-definable" , "EmptySet-Definable".
Also please see , for last part of your question , "constructable sets" and their relation between "definable sets" in...
First Post .
Also note the following:
AxB={(x,y): x€A and y€B} .
Thus the elements of AxB are of form {x,{x,y}} .
By you can derive , if my memory is still good ,
AxB is a subset of P(P(A union B)) where P denotes the powerset map .