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Some older books use the terms real variable and apparent variable for free variable and bound variable, respectively. A free variable is a notation (symbol) that specifies places in an expression where substitution may take place and is not a parameter of this or any container expression.
Affixes are bound by definition. [5] English language affixes are almost exclusively prefixes or suffixes: pre-in "precaution" and -ment in "shipment". Affixes may be inflectional, indicating how a certain word relates to other words in a larger phrase, or derivational, changing either the part of speech or the actual meaning of a word.
The derivative of a constant term is 0, so when a term containing a constant term is differentiated, the constant term vanishes, regardless of its value. Therefore the antiderivative is only determined up to an unknown constant term, which is called "the constant of integration" and added in symbolic form (usually denoted as ).
Thus an expression represents an operation over constants and free variables and whose output is the resulting value of the expression. [ 22 ] For a non-formalized language, that is, in most mathematical texts outside of mathematical logic , for an individual expression it is not always possible to identify which variables are free and bound.
A quantifier has a scope, and an occurrence of a variable x is free if it is not within the scope of a quantification for that variable. Thus in ((,)) (,) the occurrence of both x and y in C(y, x) is free, while the occurrence of x and y in B(y, x) is bound (i.e. non-free).
As this example shows, when like terms exist in an expression, they may be combined by adding or subtracting (whatever the expression indicates) the coefficients, and maintaining the common factor of both terms. Such combination is called combining like terms or collecting like terms, and it is an important tool used for solving equations.