What does it mean if a variable is free?

What does it mean if a variable is free?

In computer programming, the term free variable refers to variables used in a function that are neither local variables nor parameters of that function. The term non-local variable is often a synonym in this context.

Can a free variable be any value?

You can take ANY variable as free. When you row reduce your system of equations, you may end up with equations that have more than one variable. In this case, the free variables are those who can choose to have any value; the other variables will then depend on the values of the free variables.

Does a free variable mean no solution?

Whenever a system has free variables, then the system has infinitely many solutions.

What is a free variable in logic?

A variable is free in a formula if it occurs at least once in the formula without being introduced by one of the phrases “for some x” or “for all x.” Henceforth, a formula S in which x occurs as a free variable will be called “a condition…

What is free variable of a system of linear equation?

A free variable is a parameter that is not a leading variable. A leading variable is the first variable that has a non-zero coefficient in reduced form. These definitions are most easily understood with respect to the Echelon form of a system of linear equations expressed as a Matrix.

Why do free variables have infinite solutions?

A system of m×n linear homogeneous equations with one unknown missing has at least one free variable, hence an infinite number of solutions. Therefore, such a system always has the zero solution and also a nonzero solution.

Does a free variable mean linear dependence?

This violates the necessary and sufficient condition that all the variables must be zeros in order for the linear combination to be equal to zero. Thus, the presence of a free variable forces your set to be linearly dependent immediately from the definition.

What is a free variable in first order logic?

A variable that is not bound is called free. Notice that formulas in first-order logic say things about their free variables. For example, in the interpretation we have in mind, the formula ∀y(x≤y) says that x is less than or equal to every natural number.

What is a free variable in programming?

The idea is related to a placeholder (a symbol that will later be replaced by some literal string), or a wildcard character that stands for an unspecified symbol. In computer programming, the term free variable refers to variables used in a function that are neither local variables nor parameters of that function.

What is the difference between pivot and free variable?

x, y and z can take values of any combination and are called free variables. a, b and c are dependent on the above free variables (x, y and z) and cannot be any combination. a, b and c are called pivot or leading variables. One more thing, depending upon how we form the above equations the pivot and free variable might be changed.

How do you know if a variable is free or bound?

For this reason, the same variable x can be either free or bound depending on which fragment of code you are talking about. If the fragment contains the variable’s binding site (for example, it is listed in the function arguments) then it is bound, if not, it is free.

What is the value of a free variable at compile time?

The value of a free variable can not be generally determined at compile time, since is heavily determined by the run time flow and the call stack. Whether a variable is free or bound is relative; it depends on the fragment of code you are looking at. In other words, freeness is a property of the context.