you refer to variables like “x” “y” “z” so on so forth, but what happens when you run out? Do you go capital do you use a special symbol or something?
In: Mathematics
Variables in what exactly? Math? Programmin? Some things else?
On a more practical side, you’d run out of human comprehensibility far far quicker than you’d ever run out of symbols.
It would be rare to find equations requiring more than a half dozen to a dozen variables. It is more useful to classify and break down a complicated relationship into sub-relationships and equations. Human minds (IMHO) cannot comprehend 8-9 variables in a single equation in anything other than very simple relationships. Equations are meant to communicate, to explain and educate. Writing something down that most people could not grasp simply because of it’s lack of conciseness is the opposite of communication.
In general they get recycled and can be context dependant. as an example the greek letter sigma has different uses in structural mechanics, image processing, and sensor data processing. What it means depends on which one your working with.
Using subscripts and superscripts is common as well, especially when the variables are somewhat standardized. These can be other letters, numbers, words or abbreviations and can be chained together.
Yes, both of those things, there are many constants and variables expressed as capital letters, greek letters and other symbols.
You can also use subscripts, a lot of time based equations or something iterative with use like T0, T1, T2 etc… with the number as a subscript.
There’s hundreds of acknowledged symbols, and those can be modified with stuff like subscripts.
Even the most complex equation you’d ever deal with isn’t going to have like 200 different variables.
And if any equation did ever have that, you can create terms that equal another equation.
In some Equations, like the Black-Scholes equation in Finance there’s two values that actually refer to the solution to another equation.
So you can Say X = Y + Z where Z = A + B + C
So you’d never be able to run out.
Depends. Using a notation like a1, a2,…. is a way to do it. I come from the practical side, where variables are associated with physical properties. If in doubt, we mostly use subscript or superscript explanations what the specific one means. For example E is energy, E^0 is the standard potential of an electrode, E°cell is the standard potential of the whole cell and so on.
You can literally use anything. Letters, symbols, Greek letters, Asian characters, doodles, words, etc etc etc. They’re just placeholders.
The equation E=mc^2 can just as accurately be written Kumquat=$£^2 as long as all parties agree what the terms mean
It doesn’t really matter since we are just talking about notation. You could use stick figures to represent your variables and it would all still work the same.
But conventionally you see a lot of Greek letters, often with discipline-specific meanings.
Ultimately if you need an inexhaustible pool of variables to choose from you can just use letters with subscript numbers (X1, X2 etc. except those numbers should be subscripted and i can’t do that in reddit)
You trade out the individual variables for a sequence. Instead of a, b, c, …, z, you’d just have a_1, a_2, a_3, …, a_26. Since the subscripts can go as high as you want, you effectively have an infinte number of variables.
First of all, you can always use lowercase letters, uppercase letters, and quite commonly Greek letters.
But you can also use subscripts (e.g. a1, a2, a3…). For example, look at the [definition of polynomial](https://en.wikipedia.org/wiki/Polynomial#Definition).
You can also add a diacritical mark to the variables, like ã and ā. This usually denotes a variable that is related to or derived from an existing variable.
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