One and only one

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In mathematics and logic, the phrase "there is one and only one" is used to indicate unique existence, i.e. it is the unique existential quantifier, represented by the symbol ∃! . The term exactly one, which can strike non-specialists as odd, is also used. The use of this phrase in connection with quantification is preferable to that of the less precise "one" or "a"; for example, "Every positive real number has a positive real root" is true, but "Every positive real number has one and only one positive real root" is more accurate, especially given that there exist many roots which are not real numbers, or not positive.

[edit] See also

• Mathematical jargon
• Square root
• Radical (mathematics)