Well, the variables in those eqtoaiuns are still just ordinary variables, and you can rename them to whatever and still have the same result the graph on the is just one way of what the equation meansTake, say, x^2 + y^2 = 1. This is just an equation, it’s valid for some values of x and y, and invalid for others. Now, there’s too many values that it’s valid for to just list them all (there’s an infinite number, after all), so one way is to take those x’s and y’s and plot them as points on a cartesian plane and it just so happens that when you do that, you get a circle. Now, this circle is just a way of representing the equation, but this often gets simplified away in school to say that the equation *is* the circle.The technical terms are that the equation is the locus of the circle, and that the circle is the graph of the equation. The circle consists of all the points that satisfy your equation.But, if you’re not working directly with the graph itself in a proof, you can still replace all the x’s and y’s with p’s and q’s and you’ll still have the same result. It’ll just be less obvious to whoever’s reading the proof, that this equation corresponds to that graph. Conventions, like using x/y/z for locations, k for constants, n for integers, z for complex they’re just conventions, and don’t have any bearing on whether a proof is valid or not but following them will make it easier for someone reading the proof to quickly see what you’re talking about.
Well, the variables in those eqtoaiuns are still just ordinary variables, and you can rename them to whatever and still have the same result the graph on the is just one way of what the equation meansTake, say, x^2 + y^2 = 1. This is just an equation, it’s valid for some values of x and y, and invalid for others. Now, there’s too many values that it’s valid for to just list them all (there’s an infinite number, after all), so one way is to take those x’s and y’s and plot them as points on a cartesian plane and it just so happens that when you do that, you get a circle. Now, this circle is just a way of representing the equation, but this often gets simplified away in school to say that the equation *is* the circle.The technical terms are that the equation is the locus of the circle, and that the circle is the graph of the equation. The circle consists of all the points that satisfy your equation.But, if you’re not working directly with the graph itself in a proof, you can still replace all the x’s and y’s with p’s and q’s and you’ll still have the same result. It’ll just be less obvious to whoever’s reading the proof, that this equation corresponds to that graph. Conventions, like using x/y/z for locations, k for constants, n for integers, z for complex they’re just conventions, and don’t have any bearing on whether a proof is valid or not but following them will make it easier for someone reading the proof to quickly see what you’re talking about.