Mathematics Axiomatic Frontier and How Outer Worlds Puncture it to Generate Numbers.

Any number within Mathematical World (bounded by ZFC Axiomatic Frontier, including Axiom of Choice :-) is seen within Math World as generated directly from the Fundamental Axioms. But, applied mathematicians and other people using math within their disciplines (Civil Engineers, Traders, Physicist, as shown in this illustration) have to keep tab what they have just counted, i.e. what a particular number is associated with, and where it comes from. And that, the language, the particular discipline's language and logic, as it is illustrated, is outside mathematics, and that fact should be signified to students when introducing them to math. There has to be a clear distinction between a particular discipline discourse, discipline's specific logic, language of explanation, definitions, and pure math, math that can be traced, essentially, to the fundamental ZFC axioms.

Each thin arrow that goes from "Outer" world, world where the math is "applied", can generate a number, inside Math world, can generate a relationship, formula, even differential and integral equation, right there. When the calculation is done, within Math, the result will be returned via thick arrow to the discipline where the "request" for calculation came from.

The drawing shows one more property. Math is not "applied" to the fields, but, it's rather used as a direction of thinking in order to solve some particular problem. The world "applied" probably came in use because the mathematical constructs, and math development in general, can be done without any of the Outer World "bubbles", disciplines (Economics, Physics, Civil Engineering, Electrical Engineering), and then, when there is a need, that math results can be matched with some requests from the Outer World. While certain domains of math development have been motivated by physical processes, that math can be developed completely from mathematical axioms, without analyzing any physical process.

Here are more links you might like as well:

Any number within Mathematical World (bounded by ZFC Axiomatic Frontier, including Axiom of Choice :-) is seen within Math World as generated directly from the Fundamental Axioms. But, applied mathematicians and other people using math within their disciplines (Civil Engineers, Traders, Physicist, as shown in this illustration) have to keep tab what they have just counted, i.e. what a particular number is associated with, and where it comes from. And that, the language, the particular discipline's language and logic, as it is illustrated, is outside mathematics, and that fact should be signified to students when introducing them to math. There has to be a clear distinction between a particular discipline discourse, discipline's specific logic, language of explanation, definitions, and pure math, math that can be traced, essentially, to the fundamental ZFC axioms.

Each thin arrow that goes from "Outer" world, world where the math is "applied", can generate a number, inside Math world, can generate a relationship, formula, even differential and integral equation, right there. When the calculation is done, within Math, the result will be returned via thick arrow to the discipline where the "request" for calculation came from.

The drawing shows one more property. Math is not "applied" to the fields, but, it's rather used as a direction of thinking in order to solve some particular problem. The world "applied" probably came in use because the mathematical constructs, and math development in general, can be done without any of the Outer World "bubbles", disciplines (Economics, Physics, Civil Engineering, Electrical Engineering), and then, when there is a need, that math results can be matched with some requests from the Outer World. While certain domains of math development have been motivated by physical processes, that math can be developed completely from mathematical axioms, without analyzing any physical process.

Here are more links you might like as well:

- Real world examples for rational numbers, for kids
- Math and its relationship with real world
- How math can be applied to so many different fields?
- Where the graphs in mathematics and physics come from?
- Tweets about math, physics, and how to approach math calculations
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- Comparison between making movies and math and physics
- More tweets about math
- Domains of math applications and math development
- Where all those number series in math are coming from?
- How to understand the role of math in economics, physics, engineering, and in other fields

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