Suppose you are given the statement 'there exists x in the real numbers such that x^2-2=0' Would you say the x is a variable or a constant? There are two solutions for x so in this case x is a variable? But what if you're given 'there exists x in the real numbers such that x-2=0' There is only one solution, x=2. Would you say x is a variable or a constant? What happens if it's the statement 'there exists (x,y) in the real numbers such that x^2+y^2=0'? Are x and y treated as variables or constant? It seems variables is the more likely answer. In all cases, x does seem to act like variables because they could be any real number with the condition that they satisfy the equation.