This question calls for a mathematically sound & intuitive explanation of SQL joins that clearly shows the difference between the following:
- Inner Join
- Left Join
- Right Join
- Full Outer Join
The explanation of joins should not misuse Venn diagrams. This is key. It should also be as accessible as possible to a computer programmer or mathematical beginner. We don't want to scare programmers away from mathematical concepts by using too much jargon. Of course, a little bit of maths is always necessary.
The internet is rife with usages of Venn diagrams to explain SQL joins. As pointed out in the following articles, this leads to a grave misunderstanding of either Venn diagrams, SQL joins or both:
As a website that many students of mathematics and computer science consult as a source of truth, it is our responsibility as a community to try everything in our power to propagate truth. Unfortunately, Venn diagram usage to explain a concept which is really Cartesian product at its core is all to rife.
Our own sister site, StackOverflow, is unfortunately part of this problem: https://stackoverflow.com/questions/38549/what-is-the-difference-between-inner-join-and-outer-join/38578#38578. While there are many amazing answers under that question, the prevailing belief on that site appears to be that joins are intersections/unions and Venn diagrams are appropriate to explain them. The top ranked and accepted answer uses Venn diagrams and intersection/union to explain joins.
While there may be some cases where join coincides with intersections and unions, it is not in general the case. I fear that people are simply seeing the special case and accepting the Venn diagram explanation. I fear they are then walking away with improper understanding of SQL joins and set theory.
I am hoping that by posting a question here, even a small percentage of people might be directed here instead of to another site that has SQL joins incorrectly explained using Venn diagrams. I am hoping that at least one of the Stack Exchange websites can have an accepted answer explaining SQL joins that is mathematically accurate, and potentially many other good alternative answers alongside it to provide different perspectives.
To be clear: I think I understand SQL joins myself. The purpose of this question is to create visibility and a source of truth for those new students of computer science and mathematics who might not understand them fully.