In mathematics, what is the difference between a constant and a variable?

Question

I am not talking about the terms "constant" or "variable" in the context of computer science or the scientific method for performing experiments. I am talking about these terms in the context of pure mathematics.

I know that the value of a constant does not change within the scope of a problem or set of problems, although the same symbol used as a constant may have a different value in a new problem. The term "constant" should not be confused with a "mathematical constant", such as pi or the number e (Euler's constant), which signify quantities that never change regardless of the context.

I also know that a variable may be assigned a value, just as a constant can be assigned a value for a given set of problems. But if both constants and variables can be assigned any value, what is the difference between constants and variables?

Is the difference just that the scope of a variable is different? If so, how?

Can a variable have more than one value at the same time?

What does it mean for a variable to have or represent more than one value?

Can a constant be unknown, or are variables the only mathematical entities with the property of being unknown?

Answer 1

A constant's value never changes. 1 always equals 1; therefore, 1 is a constant. From one problem or set of problems to the next, 1 will always equal 1. "x", on the other hand, might not; therefore, x is a variable.

Answer 2

Constants are values that don't change within an equation

Sp. when you see something like "ax^2 + bx + c" in a function, the a, b, c are constants. they represent general values that "scale" the term after them. You might not know the value, of them until you see the actual function (like "2x^2 + 3x + 4"), but, until you know what they are, you treat them as if the values never change.



the "x" in these functions is a variable. The function applies to all the values that "x" can take (that is, the "domain") there can be more than one variable in a function: as in x^2 + y^2 = 1.



pi, phi, Phi, e, i and such like are special values. They are "scalars" that are so common that they have been given specific symbols, but you can treat them (in most cases) exactly like the a, b, c, in the function above.



Often, you can have constants that are not known. For example, you might be told that "x is proportional to y" this, mathematically means that there is a constant such that x = (a constant) times y. If it's inversely proportional, then you get the meaning that x = (a constant)/y. You can get round these by realising they mean that x / y = (a constant) if they are proportional or x * y = (a constant) if they are inversely proportional. Often, if you have a multiple pairs in these cases, you don't even need to know the value of the constant, so it's enough just to know the constant exists.

Answer 3

To elaborate on your additional details edit, the values "a", "b", and "c" in a polynomial expression are constants that must be calculated by hand; there values are definite, but may not be known based on whether you have coordinates to input or not.



I see what you mean when you say that you can pick any value you like for a, b, c, or x; but normally that won't lead anywhere as the general point of a polynomial expression is to fit a data-set with the optimal approximation curve whether it be extrapolated or interpolated.



In coordinates of the form (x,y), x represents the variable x, while y represents a value that was calculated through a given function. Arbitrarily picking the constant values from which y would be calculated results in an entirely different data-set; in short, x calls a certain value of the function and the constants are scalars which define the function.

Answer 4

What Are Constants In Math

Answer 5

A variable is a sign rather than a number e.g. π or x.



A constant is a number in an equation without any variables attached to it.