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In mathematics, an equaliser is a set of arguments where two or more functions have equal values. An equaliser is the solution set of an equation. In certain contexts, a difference kernel is the equaliser of exactly two functions. == Definitions == Let ''X'' and ''Y'' be sets. Let ''f'' and ''g'' be functions, both from ''X'' to ''Y''. Then the ''equaliser'' of ''f'' and ''g'' is the set of elements ''x'' of ''X'' such that ''f''(''x'') equals ''g''(''x'') in ''Y''. Symbolically: : The equaliser may be denoted Eq(''f'',''g'') or a variation on that theme (such as with lowercase letters "eq"). In informal contexts, the notation is common. The definition above used two functions ''f'' and ''g'', but there is no need to restrict to only two functions, or even to only finitely many functions. In general, if F is a set of functions from ''X'' to ''Y'', then the ''equaliser'' of the members of F is the set of elements ''x'' of ''X'' such that, given any two members ''f'' and ''g'' of F, ''f''(''x'') equals ''g''(''x'') in ''Y''. Symbolically: : This equaliser may be written as Eq(''f'',''g'',''h'',...) if is the set . In the latter case, one may also find in informal contexts. As a degenerate case of the general definition, let F be a singleton . Since ''f''(''x'') always equals itself, the equaliser must be the entire domain ''X''. As an even more degenerate case, let F be the empty set {}. Then the equaliser is again the entire domain ''X'', since the universal quantification in the definition is vacuously true. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Equaliser (mathematics)」の詳細全文を読む スポンサード リンク
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