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And, substitution allows one to derive restrictions on the possible values, or show what conditions the statement holds under. For example, taking the statement x + 1 = 0 , if x is substituted with 1 , this implies 1 + 1 = 2 = 0 , which is false, which implies that if x + 1 = 0 then x cannot be 1 .
In optical fiber technology, the substitution method is a method of measuring the transmission loss of a fiber. It consists of: using a stable optical source, at the wavelength of interest, to drive a mode scrambler, the output of which overfills (drives) a 1 to 2 meter long reference fiber having physical and optical characteristics matching those of the fiber under test,
Change of variables is an operation that is related to substitution. However these are different operations, as can be seen when considering differentiation or integration (integration by substitution). A very simple example of a useful variable change can be seen in the problem of finding the roots of the sixth-degree polynomial:
Substitution (logic), a syntactic transformation on strings of symbols of a formal language; String substitution, a mapping of letters in an alphabet to languages; Substitution of a character in a string, one of the single-character edits used to define the Levenshtein distance; Substitution cipher, a method of encryption
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In calculus, integration by substitution, also known as u-substitution, reverse chain rule or change of variables, [1] is a method for evaluating integrals and antiderivatives. It is the counterpart to the chain rule for differentiation , and can loosely be thought of as using the chain rule "backwards."