I would be really grateful if someone could do this in a succinct manner that I, as a non statistician, can easily understand.
I never came across Cartesian sets although I did mathematics all my life. Do you mean Cartesian products of sets?
I never came across Cartesian sets although I did mathematics all my life. Do you mean Cartesian products of sets?
If you mean Cartesian product of sets then
Consider two the Sets A and B, the cartesian product (set) of A and B denoted by
A x B is the set of all ordered pairs (a,b) such that a is in A and b is in B.
for example if A = {a1,a2} and B = {b1,b2,b3} then
A x B = {(a1,b1),(a1,b2),(a1,b3),(a2,b1),(a2,b2),(a2,b3)}
hope it helps!
Thank you both, in facet theory (a social science methodology) reading a rather old texts I came across the phrase of a component set acting or playing in the role of a Cartesian set. What I understand this to mean is a selected set of variables acting as or being taken to represent all possible combinations in a set. What do you think?
Is what I describe seizable to you as a cartesian product (set)? It doesn't feel right to me nut I am not a mathematician.
I think the only way to clarify the case is that you give us a larger fraction of the text in question.
Well, there should be at least two sets for which you want a representation for. In this case your Cartesian set will be the possible combinations of the two sets in a certain order as described in my previous post.
I cannot find the quotation I stated originally, so perhaps I recalled this incorrectly. However, I am attaching a snippet from representative text.
I have now found the source of “a set playing the role of a component set of a Cartesian set.” (Shye, 1978, p412). I may have a copy of this book in my office.
I should add the book is: Theory Construction and Data Analysis in the Behavioral Sciences, San Francisco: Jossey-Bass.
Paul, your text snippet makes the matter clear:
Facet theory deals with Cartesian products of finitely many finite sets. Facets are, subsets of such Cartesian products.
The author of this text snippet is obviously not educated in using the mathematical language properly. Otherwise he could not write blunder such as "a facet is simply (writing 'simply' if something is not completely clear to the writer is still in wide-spread use) a set involved in a Cartesian product". It can be either an element of ..., or a subset of ..., but never 'involved'. Since he calls a facet a set, I infer (not by logic but only by experience how non-mathematicians used to think in 1958 -- many of my physics professors gave such bad examples) that he means subset. Although he does not say it here, one can expect that he will speak of his facets as Cartetesian sets (since they are related to Cartesian products and the name is impressive). This then would be by misuse of language and would not refer to a well defined mathematical concept.
Unfortunately books written by such language misusers sometimes contain valuable material so that the self-suggesting advice to ignore all the stuff as blunder may be not a wise one.
Yes, there are many examples of using a mathematical term in a different sense by people who are not perhaps aware that the term is already in use to mean something quite different. For example, the term 'characteristic function' is used in two completely different senses in Measure Theory and in Statistics.
- Badges
- Science topic
- Similar topics
- Mathematical Sciences
- Algebra