System to represent objects in Mathematics

[FactChecker]

Based on some of your recent threads, you are not very far along in your mathematics studies.

Fortunately, @pairofstrings has given us his level of education (working on undergrad) in his profile. I really appreciate that. So many do not give any information. I would say that it is time for him to start including as many math classes as possible before he graduates.

 

[Mark44]

I would say that it is time for him to start including as many math classes as possible before he graduates.

Strongly agree.

 

[jonk75]

$\mathcal{C}=\{\,(x,y)\in \mathbb{R}\,|\,x^2+y^2-1=0\,\}$

In the above, it should be $(x,y)\in \mathbb{R}^2$.

 

[pairofstrings]

Okay. I want to be able to write equations and I am working towards it.

Thanks everyone.

 

[fresh_42]

In the above, it should be $(x,y)\in \mathbb{R}^2$.

Indeed. I corrected it, thank you.

 

[Mark44]

Okay. I want to be able to write equations and I am working towards it.

Which has nothing as far as I can see with what you said at the start of this thread:

Usually, Computer Programmers use Flow Charts, Algorithms, or UML diagrams to build a great software or system. In the same manner, in Mathematics, what do Mathematicians use to build a great system that they want to build.

 

[jbriggs444]

Okay. I want to be able to write equations and I am working towards it.

An important ingredient for writing something down is having something to say. If one has something to say and lacks a notation in which to say it elegantly, then it is time to worry about inventing notation.

 

[FactChecker]

In short, I want to know the System in Mathematics that let's me communicate my ideas with other mathematicians.

If you want to communicate with other mathematicians, the first thing to do is to read their work and learn whatever is necessary to understand what they are saying. Don't expect millions of others to learn your system rather than you learning their standard, common language.

 

[fresh_42]

Don't expect millions of others to learn your system rather than you learning their standard, common language.

And this existing language is the reason why we can talk here on PF literally around the globe. Physicists and mathematicians don't have the least difficulties to cooperate, at least no scientific obstacles. English is only the carrier wave, the messages are written in mathematics and everybody can understand them, regardless of any cultural background. Set theory, predicate logic and arithmetic must be quite strong tools already.