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2. Free variables and bound variables - Wikipedia

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

   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. This nested, inner binding of x is said to "shadow" the outer binding. Occurrences of x in U are free occurrences of the new x. [3]

3. MathOverflow - Wikipedia

   en.wikipedia.org/wiki/MathOverflow

   MathOverflow is a mathematics question-and-answer (Q&A) website, which serves as an online community of mathematicians. It allows users to ask questions, submit answers, and rate both, all while getting merit points for their activities. [1] It is a part of the Stack Exchange Network, but distinct from math.stackexchange.com.

4. Substitution (logic) - Wikipedia

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

   Considering mathematics as a formal language, a variable is a symbol from an alphabet, usually a letter like x, y, and z, which denotes a range of possible values. [7] If a variable is free in a given expression or formula, then it can be replaced with any of the values in its range. [8] Certain kinds of bound variables can be substituted too.

5. Gross substitutes - Wikipedia

   en.wikipedia.org/wiki/Gross_substitutes

   In auction theory and competitive equilibrium theory, a valuation function is said to have the gross substitutes (GS) property if for all pairs of commodities: () (). I.e., the definition includes both substitute goods and independent goods , and only rules out complementary goods .

6. Extraneous and missing solutions - Wikipedia

   en.wikipedia.org/wiki/Extraneous_and_missing...

   Because of this, often, the only simple effective way to deal with multiplication by expressions involving variables is to substitute each of the solutions obtained into the original equation and confirm that this yields a valid equation. After discarding solutions that yield an invalid equation, we will have the correct set of solutions.

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8. Integration by substitution - Wikipedia

   en.wikipedia.org/wiki/Integration_by_substitution

   Integration by substitution can be derived from the fundamental theorem of calculus as follows. Let and be two functions satisfying the above hypothesis that is continuous on and ′ is integrable on the closed interval [,].

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