System to represent objects in Mathematics

Thanks.

Mark44
Mentor
It could as well be the union on sets or the OR in Boolean algebras
Yep, I thought of those as well, but my list seemed long enough already to make my point.

fresh_42
fresh_42
Mentor
Yep, I thought of those as well, but my list seemed long enough already to make my point.
And the list of multiplications isn't any shorter.

FactChecker
Gold Member
If you have never had abstract algebra, you should look at that. It studies addition and multiplication in very abstract terms. That is the only way to realize what is essential for those operations to make sense and what is not essential.

Mark44
Mentor
I'm curious and I want a PhD. in Mathematics.
It's good to have goals, but in order to attain them, you need to have a realistic plan of action and follow through on it. Based on some of your recent threads, you are not very far along in your mathematics studies.

In this thread, you weren't clear on the difference between measures of length vs. area -- https://www.physicsforums.com/threa...way-into-formula-of-area-of-rectangle.778700/
Questions like these suggest that you aren't very far along in mathematical knowledge, so getting a PhD will be a long road.

FactChecker and fresh_42
FactChecker
Gold Member
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
Mentor
I would say that it is time for him to start including as many math classes as possible before he graduates.
Strongly agree.

FactChecker
##\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##.

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

Thanks everyone.

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fresh_42
Mentor
In the above, it should be ##(x,y)\in \mathbb{R}^2##.
Indeed. I corrected it, thank you.

jonk75
Mark44
Mentor
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
Homework Helper
2019 Award
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
FactChecker
Gold Member
In short, I want to know the System in Mathematics that lets 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
Mentor
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.

FactChecker