Assuming you have $n$ variables, how many maximum independent satisfiable constraints can you have? What I mean by independent is that the equations all express unique constraints, s.t for example $x + y = 2$ and $2x + 2y = 4$ would not count as two unique constraints.
My thinking is that outside of mathematics, you can have as many satisfiable constraints between elements of a set as there are non-mutually exclusive relationships between those elements.
For example, let's say we're talking about two people $A$ and $B$. You could say that you want to find two people such that $A$ is taller than $B$, and $B$ is richer than $A$, and $A$ is stronger than $B$, and $A$ is hairier than $B$, etc...
However, let's say you have two variables $x$ and $y$. If we for now constrain ourselves to the real numbers and all of the operations we have on that set, it seems from what I remember being told in school (and I can't find a counterexample), that even though we have many different kinds of operators and ways to express numbers (powers, exponents, logs, addition, multiplication, etc...), we can't have more unique satisfiable constraints than we have variables.
Is this always true? (what about if we add complex numbers?)
Is there an intuitive way to understand why (whether or not it's true)?
Does it say something about common fundamental nature between certain operators as far as the kind of relationship they express?