- by kq4ym, Data Doctor
- 7/21/2015 9:29:34 AM
Yes, a good explanation of the numbers, sets, duples, relation, etc. Because there's often a lack of understanding of the basics by sofware package users, may there should be an introduction included with those handed the software and expected to get results quickly?
- 7/14/2015 4:00:42 PM
A more formal way of saying it is that numbers are abstract and we assign meaning to them when we APPLY them to some aspect of the real world.
Similarly, we apply relations to database management, but adapting them as R-tables to it. R-tables are relations applied to databases and adapted accordingly. Stay tuned.
It's the mathematics that guarantee PROVABLY logically correct query results. That's the importance of RDM and any violation thereof loses the guarantee. Both database designs and SQL DBMS's violate the RDM left and right.
- 7/9/2015 9:50:14 PM
Numbers are abstract -- they don't have inherent MEANING; we assign meaning to them, we apply them to real world aspects. So are domains and relations.
I am glad I made it clear to you.
Exactly right: most practitioners use tools without a good grasp of the fundamentals and the extent to which they adhere to or violate them.
- 7/9/2015 8:35:08 PM
I see. Numbers do not have any inherent value in and of themselves, they only have value to which they are assigned. That makes complete sense to me. Also thank you for your beautifully clear explanation of domains, tuples and relations. I am saving this because it is quite frankly the clearest explanation I have read in quite some time.
Kudos to you and your expertise, may we all be so clear minded ! Looking forward to more from you in this area. I get the feeling many hide behind software packages without any true understanding of what they are doing - especially when it comes to databases.
- 7/9/2015 7:29:09 PM
The number 1 per se does not represent anything in the real world. We can ASSIGN meaning to it: 1 person, 1 job, 1 car, 1 shipment and so on. When we assign meaning to numbers we APPLY them to some aspect of the real world. Regardless of what meaning we assign to numbers, arithmetic operations and their results do not depend on the meaning e.g. 1+1=2 whether they represent persons or jobs.
A domain is a set--a pool of values--that per se does not have any real world meaning e.g. all values between 10,000 and 1.000.000. We can apply it to some real world aspect by assigning meaning to it e.g. the possible range of salaries in an enterprise.
If we have 6 domains and we choose one value from each we get a tuple, which is also a set. We can assign meaning to it e.g. attributes of some employee.
A relation is a set of tuples. We can assign meaning to it: the properties of a set of employees.
In the same manner in which we apply numeric algebra--arithmetic--to numbers, we apply relational algebra to relations. Its operations and results do not depend either on the meaning we assigned to relations.
- 7/9/2015 5:53:27 PM
"...Think now of the algebra of numbers, arithmetic. Numbers are abstractions -- they do not have any inherent meaning."
Thanks Fabian for covering Database Fundamentals, I was just thinking of this topic so I am glad a person of your expertise has taken on the challenge. While I was wrestling with domains and tupels, the above statement really caught my attention.
Numbers have No inherent meaning ? Well for the sake of a simplistic example, the number one is not the number nine nor vice-versa even if it is confined to simple Algebra, so I would argue numbers do have inherent meaning.
Am I missing the point ? Taking this out of context ? Please help me understand what is meant by this.