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  2. Free variables and bound variables - Wikipedia

    en.wikipedia.org/wiki/Free_variables_and_bound...

    Note: we define a location in an expression as a leaf node in the syntax tree. Variable binding occurs when that location is below the node n. In the lambda calculus, x is a bound variable in the term M = λx. T and a free variable in the term T. We say x is bound in M and free in T. If T contains a subterm λx. U then x is rebound in this term.

  3. Dependent and independent variables - Wikipedia

    en.wikipedia.org/wiki/Dependent_and_independent...

    In mathematics, a function is a rule for taking an input (in the simplest case, a number or set of numbers) [5] and providing an output (which may also be a number). [5] A symbol that stands for an arbitrary input is called an independent variable, while a symbol that stands for an arbitrary output is called a dependent variable. [6]

  4. Variable (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Variable_(mathematics)

    Free variables and bound variables A random variable is a kind of variable that is used in probability theory and its applications. All these denominations of variables are of semantic nature, and the way of computing with them ( syntax ) is the same for all.

  5. Quantifier (logic) - Wikipedia

    en.wikipedia.org/wiki/Quantifier_(logic)

    Bound and free variable occurrences are colored in red and green, respectively. An interpretation for first-order predicate calculus assumes as given a domain of individuals X. A formula A whose free variables are x 1, ..., x n is interpreted as a Boolean-valued function F(v 1, ..., v n) of n arguments, where each argument ranges over the domain X.

  6. Exercise (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Exercise_(mathematics)

    In college mathematics exercises often depend on functions of a real variable or application of theorems. The standard exercises of calculus involve finding derivatives and integrals of specified functions. Usually instructors prepare students with worked examples: the exercise is stated, then a model answer is provided. Often several worked ...

  7. Indicator function - Wikipedia

    en.wikipedia.org/wiki/Indicator_function

    The notation is used in other places as well, for instance in probability theory: if X is a probability space with probability measure and A is a measurable set, then becomes a random variable whose expected value is equal to the probability of A:

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