I'm trying to write a simple formula based on some work I've had to do with programming. In programming, I have the ability to write a class with certain properties. For example: A coordinate with x & y values.
I can then access these values like… point.x & point.y
What is the correct way to describe these objects and use their values in mathematical notation?
Best Answer
The dot-notation is not common in Maths. Instead, you usually use indices, where the order of element and property might be reversed. Thus, $element.property$ is usually referred to as $property_{element}$, where any name is usually single-lettered, and elements are also often identified by some number.
For example let $M=\{point1, point2\} $ be some set of two points, both with properties x and y. In the programming lanuage you would refer to them by point1.x, point1.y, point2.x, point2.y.
In Maths, you would usually identify the two points with numbers, thus, $M = \{1, 2\}$, and write $x_1, y_1, x_2, y_2$. But things can also be totally different, depending on how it is most comfortable for your purpose.
It is also ok to write $p_x$, $p_y$ for any $p \in M$, where it might be that $p = point1$ or $p = point2$.
Another alternative: it is always possible to represent properties by a function on the set of elements (just as properties can also be accessed with a function, e.g., point1.getX()). Thus, we could define the function $x : M \rightarrow \mathbb{R}$ to map to the x-coordinate of any given point from the set $M$ to its real value, and refer to it by writing $x(p)$ for any $p \in M$.
However, the universal answer to this question is that there is no universal answer :)