# Cartesian product and relationship

### Cartesian product - Wikipedia

Bitopological Spaces: Theory, Relations with Generalized Algebraic Structures, . For any Cartesian product of n sets, the relations are called n-dimensional. Secondly is that relationships that use a cartesian join cannot have records created via them. If you have a portal where you want to achieve. Relation: A subset of Cartesian product. A relation R from set A to set B is a subset of the Cartesian product A × B. The subset is derived by describing a.

There is also a geometric interpretation of the cross product.

**[Discrete Math 1] Cartesian Products and Ordered Pairs**

There should be a natural question at this point. First, as this figure implies, the cross product is orthogonal to both of the original vectors. Example 2 A plane is defined by any three points that are in the plane. Show Solution The one way that we know to get an orthogonal vector is to take a cross product. So, if we could find two vectors that we knew were in the plane and took the cross product of these two vectors we know that the cross product would be orthogonal to both the vectors.

However, since both the vectors are in the plane the cross product would then also be orthogonal to the plane. So, we need two vectors that are in the plane.

### ELI5: What is the Cartesian product of a relation? : explainlikeimfive

This is where the points come into the problem. Since all three points lie in the plane any vector between them must also be in the plane.

There are many ways to get two vectors between these points. This does give us another test for parallel vectors however. Here are some nice properties about the cross product. We will see an example of this computation shortly.

There are a couple of geometric applications to the cross product as well.

### Cartesian Product of Two Sets |Cartesian Product|Ordered Pairs|Subsets of a Set

We can use this volume fact to determine if three vectors lie in the same plane or not. If three vectors lie in the same plane then the volume of the parallelepiped will be zero.

Whether you switch to this technique or not depends on a number of factors which we'll outline below. Benefits of switching from Cartesian to Refresh Portal So the question is why would you want to switch to this if your cartesian join relationships have been working fine?

## cartesian product

Well, the answer is subjective. For some, there is no benefit, and for others there will. First benefit would be removing "hacks" from your solution. We still consider the cartesian join technique a hack and it may no longer be supported in future versions whereas Refresh Portal will. Secondly is that relationships that use a cartesian join cannot have records created via them.

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If you have a portal where you want to achieve this, then you may be better off using the Refresh Portal step if records don't correctly refresh. Lastly, you remove the need for a field in your database to act as the portal refresh however you gain a script step!

Benefits of staying with Cartesian Join It's the old saying - if it ain't broke, don't fix it. If there is no visible benefit in removing cartesian joins to refresh a relationship then why bother. Both methods appear to work exactly the same - the Refresh Portal script step doesn't do anything significantly different to a cartesian join refresh that we can see.

Another big benefit of a cartesian join refresh is that it can be triggered without a script. Because the refresh occurs when the value of the field used in the cartesian join is changed, this can be triggered using an auto-enter calculation on the cartesian join field that refreshes when any referenced field changes - no need for a script trigger.

In a lot of cases this is quite elegant and better than relying on script triggers There is also another big benefit of keeping with Cartesian Joins. The Refresh Portal script step requires an actual portal on your layout to refresh!