What It Means For A Variable To Vary
Varying, in the context of mathematical variables, does not mean change in the course of time, but rather dependence on the context in which the variable is used. This can be the immediate context of the expression in which the variable occurs, as in the case of summation variables or variables that designate the argument of a function being defined. The context can also be larger, for instance when a variable is used to designate a value occurring in a hypothesis of the discussion at hand. In some cases nothing varies at all, and alternative names can be used instead of "variable": a parameter is a value that is fixed in the statement of the problem being studied (although its value may not be explicitly known), an unknown is a variable that is introduced to stand for a constant value that is not initially known, but which may become known by solving some equation(s) for it, and an indeterminate is a symbol that need not stand for anything else but is an abstract value in itself. In all these cases the term "variable" is often still used because the rules for the manipulation of these symbols are the same.
Read more about this topic: Variable (mathematics)
Famous quotes containing the words what it means, what it, means, variable and/or vary:
“The aim of all commentary on art now should be to make works of art—and, by analogy, our own experience—more, rather than less, real to us. The function of criticism should be to show how it is what it is, even that it is what it is, rather than to show what it means.”
—Susan Sontag (b. 1933)
“Curiously enough, it seems to be only in describing a mode of language which does not mean what it says that one can actually say what one means.”
—Paul Deman (1919–1983)
“In the stress of modern life, how little room is left for that most comfortable vanity that whispers in our ears that failures are not faults! Now we are taught from infancy that we must rise or fall upon our own merits; that vigilance wins success, and incapacity means ruin.”
—Agnes Repplier (1858–1950)
“There is not so variable a thing in nature as a lady’s head-dress.”
—Joseph Addison (1672–1719)
“To know how to suggest is the great art of teaching. To attain it we must be able to guess what will interest; we must learn to read the childish soul as we might a piece of music. Then, by simply changing the key, we keep up the attraction and vary the song.”
—Henri-Frédéric Amiel (1821–1881)