Intersection of Product spaces

Click For Summary
SUMMARY

The discussion focuses on the mathematical concept of intersections of product spaces, specifically examining the relationship between (A1 ∩ A2) × (B1 ∩ B2) and (A1 × B1) ∩ (A2 × B2). It concludes that the former is strictly contained within the latter under certain conditions. Participants express confusion regarding the strict containment in intersections compared to unions, highlighting the need for clearer examples or visual aids to illustrate this concept effectively.

PREREQUISITES
  • Understanding of set theory and intersections
  • Familiarity with Cartesian products in mathematics
  • Basic knowledge of mathematical notation and symbols
  • Experience with visualizing mathematical concepts
NEXT STEPS
  • Study examples of strict containment in set theory
  • Explore Cartesian products and their properties
  • Learn about visual representations of intersections and unions
  • Investigate advanced topics in topology related to product spaces
USEFUL FOR

Mathematicians, students studying advanced set theory, educators looking to explain product spaces, and anyone interested in the nuances of mathematical intersections.

math8
Messages
143
Reaction score
0
Give an example where
(A1 intersect A2)X(B1 intersect B2) is strictly contained in (A1XB1)intersect (A2XB2).

For the union instead of the intersection I can see the reverse strict containment easily just by drawing. But for the intersection for some reason, I cannot see when the containment can be strict.
 
Physics news on Phys.org
Hi math8! :smile:

I think you're right … I think they're the same. :confused:
 

Similar threads

Proving intersection of finitely many open sets is open
  • · Replies 1 ·
Replies
1
Views
2K
Understanding First Order ODEs and Intersection of Curves
  • · Replies 4 ·
Replies
4
Views
2K
Is the Intersection of an Infinite Collection of Open Sets Always Open?
  • · Replies 5 ·
Replies
5
Views
3K
Finding three planes which intersect a point with lines
  • · Replies 1 ·
Replies
1
Views
2K
Hausdorf space condition problem
  • · Replies 11 ·
Replies
11
Views
2K
Undergrad Intersecting Planes: Is It Possible?
  • · Replies 5 ·
Replies
5
Views
2K
How Can I Find the Cubic Spline Function for This Data?
  • · Replies 1 ·
Replies
1
Views
2K
Constructing Intersection of Sets for De Morgans: Get Union of Sets
  • · Replies 4 ·
Replies
4
Views
5K
Proving the Existence of F from a Family of Finite Subsets of Natural Numbers
  • · Replies 2 ·
Replies
2
Views
2K
How to calculate all the possible combinations....?
  • · Replies 17 ·
Replies
17
Views
3K