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::Of course ''every value'' V is ''a'' solution (namely of the equation x = V). The meaning of a term is what people who use the term in general mean when they use it. That is something that cannot always be determined by juxtaposing the usual meanings of components of the term in question. A [[Welsh rabbit]] is not a rabbit that is Welsh and the [[division algorithm]] is not an algorithm. Based on how the term "extraneous solution" is used, it is clear that the terms refers to any solution V of some equation E' such that E', viewed as a proposition, is a valid consequence of an original equation E, but which value V, however, is not a solution of E. Moreover, V has to be found as a solution to E' ''in the process of attempting to solve'' E. It follows that the solutions of E are a subset of those of E'. The solution set of E' consists of the solution set of E plus, possibly, some other solutions, called ''extraneous solutions''. --[[User talk:Lambiam|Lambiam]] 15:43, 19 January 2008 (UTC)
Lambiam, on your first example, sorry, why isn't 2 a solution? [[User:Tparameter|Tparameter]] ([[User talk:Tparameter|talk]]) 16:08, 19 January 2008 (UTC)
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