The axiomatization of Quantity Calculus, the logical foundations of DA

In summary, The conversation is about the difficulty in completing the axiomatization of Quantity Calculus, despite it having only 5 basic elements and 4 concepts (Standard, Unit, Dimension, Quantity). The speaker is seeking help in examining the problem and mentions finding a formal definition of Quantity in Dimensional Analysis. They also ask about the official definition of Quantity in VIM3, where to find a definition of Dimension in Dimensional Analysis, and if ZFC set theory is appropriate for a system analogous to algebra. They also question if the fact that different entities can share the same dimensions is an obstacle to axiomatization and if there is a list of derived quantities. It is mentioned that question 3 is discussed in another thread and that
  • #1
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I was intrigued reading * http://en.wikipedia.org/wiki/Quantity_calculus" that after two centuries axiomatization of QC has not been completed, though there are only 5 basic elements and 4[3] concepts:
S[tandard],= U[nit], D[imension], Q[uantity]. I suppose nobody here has tackled the problem or knows the state of the art or can tell whether the task is unnecessary or impossible, but, with your help, I would like to examine the problem.

I tried to gather basic scientific information, I found a "formal? " definition of Q http://en.wikipedia.org/wiki/Quantity" in DA. Moreover, in the article * we read that QC... is "analogous" to a system of algebra with units instead of variables. Now, could you tell me if
1) VIM3's is the official, best definition available of Q
2) [you know or] where to find an appropriate definition of D in D[imensional] A[nalysis] and in relation to Q
3) set theory [arithmetics] ZFC is appropriate for a sistem "analogous" to algebra
4) the fact that different entities share same dimensions is an obstacle to axiomatization
5) there is a list of derived quantities
 
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  • #2
question 3) is discussed in another thread
5) I know there is a list, but I can't remember where I saw it (there were some 30 items). It is not at wiki : "list of derived quantities". This question is not important
 
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FAQ: The axiomatization of Quantity Calculus, the logical foundations of DA

1. What is the axiomatization of Quantity Calculus?

The axiomatization of Quantity Calculus is a set of axioms and rules that provide a logical foundation for dimensional analysis (DA). DA is a mathematical method used to analyze and solve problems involving units of measurement. The axiomatization helps to ensure that the calculations and solutions are mathematically consistent and accurate.

2. Why is the axiomatization of Quantity Calculus important?

The axiomatization of Quantity Calculus is important because it provides a rigorous and systematic approach to dimensional analysis. This is crucial for scientists and engineers who need to make precise and accurate measurements and calculations in their research and work. It also allows for the development of new mathematical concepts and tools for DA.

3. How is the axiomatization of Quantity Calculus used in practical applications?

The axiomatization of Quantity Calculus is used in practical applications by providing a framework for consistent and accurate unit conversions and calculations. This is particularly useful in fields such as physics, engineering, and chemistry, where precise measurements and calculations are necessary for experiments and real-world applications.

4. Are there any limitations to the axiomatization of Quantity Calculus?

While the axiomatization of Quantity Calculus is a powerful and useful tool, it does have some limitations. For example, it is based on the assumption that all measurements can be represented by real numbers, which may not always be the case in certain scenarios. Additionally, it does not account for uncertainties or errors in measurements, which can affect the accuracy of the calculations.

5. Can the axiomatization of Quantity Calculus be applied to other areas of mathematics?

Yes, the principles and concepts of the axiomatization of Quantity Calculus can be applied to other areas of mathematics, particularly those involving units and measurements. This includes fields such as economics, biology, and computer science, where dimensional analysis can be useful in solving problems and making predictions.

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