Equation Solving: Difference between revisions

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(Created page with " An Equation Solving is a Mathematics that ... * <B>See:</B> Mathematics, Number, Function (Mathematics), Set (Mathematics), Equation, [[Expressi...")
 
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#REDIRECT [[Equation Solving Task]]
An [[Equation Solving]] is a [[Mathematics]] that ...
* <B>See:</B> [[Mathematics]], [[Number]], [[Function (Mathematics)]], [[Set (Mathematics)]], [[Equation]], [[Expression (Mathematics)]], [[Equality (Mathematics)]], [[Free Variable]], [[Substitution (Logic)]], [[Identity (Mathematics)]], [[And (Logic)]], [[Solution Set]], [[Optimization Problem]].
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==References==
 
=== 2014 ===
* (Wikipedia, 2014) &rArr; http://en.wikipedia.org/wiki/equation_solving Retrieved:2014-7-26.
** In [[mathematics]], to '''solve an equation''' is to find what values ([[number]]s, [[function (mathematics)|functions]], [[Set (mathematics)|sets]], etc.) fulfill a condition stated in the form of an [[equation]] (two [[expression (mathematics)|expression]]s related by [[equality (mathematics)|equality]]). These expressions contain one or more '''unknowns''', which are [[free variable]]s for which values are sought that cause the condition to be fulfilled. To be precise, what is sought are often not necessarily actual values, but, more in general, mathematical expressions. A '''solution''' of the equation is an assignment of expressions to the unknowns that satisfies the equation; in other words, expressions such that, when they are [[Substitution (logic)|substituted]] for the unknowns, the equation becomes an [[identity (mathematics)|identity]]. <P> For example, the equation is solved for the unknown ''x'' by the solution , since substituting for ''x'' in the equation results in , a true statement. It is also possible to take the variable ''y'' to be the unknown, and then the equation is solved by . Or ''x'' and ''y'' can both be treated as unknowns, and then there are many solutions to the equation, some of which are – that is, [[and (logic)|and]] – and , and, in general, for all possible values of ''a''. <P> Depending on the problem, the task may be to find one solution – any solution will do – or all solutions. The set of all solutions is called the [[solution set]]. It is also possible that the task is to find a solution, among possibly many, that is ''best'' in some respect. Problems of that nature are called [[optimization problem]]s; solving an optimization problem is generally not referred to as "equation solving". <P> A wording such as "an equation '''in''' ''x'' and ''y''", or "solve '''for''' ''x'' and ''y''", implies that the unknowns are as indicated: in these cases ''x'' and ''y''.
 
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[[Category:Concept]]
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Latest revision as of 20:14, 26 July 2014

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