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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Uniqueness quantification ： ウィキペディア英語版 Uniqueness quantification In mathematics and logic, the phrase "there is one and only one" is used to indicate that exactly one object with a certain property exists. In mathematical logic, this sort of quantification is known as uniqueness quantification or unique existential quantification. Uniqueness quantification is often denoted with the symbols "∃!" or ∃=1". For example, the formal statement : $\backslash exists!\; n\; \backslash in\; \backslash mathbb\backslash ,(n\; -\; 2\; =\; 4)$ may be read aloud as "there is exactly one natural number ''n'' such that ''n'' - 2 = 4". == Proving uniqueness == The most common technique to proving uniqueness is to first prove existence of entity with the desired condition; then, to assume there exist two entities (say, a and b) that should both satisfy the condition, and logically deduce their equality, i.e. ''a'' = ''b''. As a simple high school example, to show ''x'' + 2 = 5 has only one solution, we assume there are two solutions first, namely, ''a'' and ''b'', satisfying ''x'' + 2 = 5. Thus :$a\; +\; 2\; =\; 5\backslash textb\; +\; 2\; =\; 5.\; \backslash ,$ By transitivity of equality, :$a\; +\; 2\; =\; b\; +\; 2.\; \backslash ,$ By cancellation, :$a\; =\; b.\; \backslash ,$ This simple example shows how a proof of uniqueness is done, the end result being the equality of the two quantities that satisfy the condition. However, that existence/expressibility must be proven before uniqueness, or else we cannot even assume the existence of those two quantities to begin with our current knowledge to date. 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「Uniqueness quantification」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.