|
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 : 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 : By transitivity of equality, : By cancellation, : 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
|