# Dictionary Definition

unique adj

1 radically distinctive and without equal; "he is
alone in the field of microbiology"; "this theory is altogether
alone in its penetration of the problem"; "Bach was unique in his
handling of counterpoint"; "craftsmen whose skill is unequaled";
"unparalleled athletic ability"; "a breakdown of law unparalleled
in our history" [syn: alone(p), unequaled, unequalled, unparalleled]

2 (followed by `to') applying exclusively to a
given category or condition or locality; "a species unique to
Australia" [syn: unique(p)]

3 the single one of its kind; "a singular
example"; "the unique existing example of Donne's handwriting"; "a
unique copy of an ancient manuscript"; "certain types of problems
have unique solutions" [syn: singular]

4 highly unusual or rare but not the single
instance; "spoke with a unique accent"; "had unique ability in
raising funds"; "a frankness unique in literature"; "a unique
dining experience"

# User Contributed Dictionary

## English

### Etymology

From unique.### Pronunciation

- Rhymes: -iːk

### Adjective

unique (comparable only in disputed usage)#### Usage notes

- Unique in its undisputed sense is not comparable. In its disputed senses, however, it can be compared as more unique, most unique, and occasionally as uniquer, uniquest.

#### Derived terms

#### Related terms

#### Translations

one of a kind

- Arabic: ,
- Czech: jedinečný
- Dutch: uniek
- Esperanto: unika
- French: unique
- German: einzigartig
- Greek: μοναδικός (monadikós)
- Korean: 독특하다
- Portuguese: único
- Russian: уникальный, исключительный, единственный
- Spanish: único, única

## French

### Etymology

From unicus.### Pronunciation

### Related terms

# Extensive Definition

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 denoted with the
symbol "∃!". For example, the formal statement

- \exists! n \in \mathbb\,(n - 2 = 4)

## Reduction to ordinary existential and universal quantification

Uniqueness quantification can be expressed in
terms of the existential
and universal
quantifiers of predicate
logic by defining the formula ∃!x P(x) to mean

- \exists x\,(P(x) \And \forall y\,(P(y) \to x = y)).

- \exists x\,P(x) \And \forall y\, \forall z\,(P(y) \And P(z) \to y = z).

- \exists x\,\forall y\,(x = y \leftrightarrow P(x)).

## Generalizations

One generalization of uniqueness quantification
is counting
quantification. This includes both quantification of the form
"exactly k objects exist such that ..." as well as "infinitely many
objects exist such that ..." and "only finitely many object exist
such that...". The first of these forms is expressible using
ordinary quantifiers, but the latter two cannot be expressed in
ordinary first-order
logic.

## See also

unique in French: Unicité (mathématiques)

unique in Dutch: Uniciteit

unique in Swedish: Unik

unique in Turkish: Biricik

unique in Chinese: 唯一量化

# Synonyms, Antonyms and Related Words

a certain, absolute, almost unheard-of,
alone, an, another, any, any one, appropriate, atomic, authentic, avant-garde,
azygous, beguiling, bewildering, beyond compare,
beyond comparison, breakaway, celibate, characteristic, creative, different, distinctive, distinguished, easily
first, either, else, enigmatic, exceptional, exclusive, extraordinary, fabulous, facile princeps,
fantastic, fascinating, first and last,
firsthand, fresh, idiocratic, idiosyncratic, imaginative, immortal, impair, in character, incomparable, incomprehensible,
inconceivable,
incredible, individual, indivisible, infrequent, inimitable, integral, intrinsic, invincible, irreducible, lone, marked, marvelous, matchless, miraculous, monadic, monistic, new, not that sort, not the same,
not the type, novel, nulli
secundus, odd, of a sort, of
another sort, of sorts, offbeat, one, one and only, only, only-begotten, original, other, other than, otherwise, outlandish, particular, passing strange,
peculiar, peerless, phenomenal, prodigious, proper, puzzling, quintessential, rare, recherche, remarkable, revolutionary, scarce, second to none, seldom
met with, seldom seen, sensational, separate, simple, single, singular, slow, sole, solid, solitary, solo, sparse, special, strange, striking, stupendous, sui generis, true
to form, unanalyzable, unapproachable, unapproached, unbeatable, uncommon, uncustomary, underived, undivided, undreamed-of,
unequaled, unexampled, unexcelled, unexpected, unfamiliar, unfrequent, unheard-of,
uniform, unimaginable, unitary, unmatchable, unmatched, unordinary, unpaired, unparagoned, unparalleled, unpeered, unprecedented, unrepeatable, unrepeated, unrivaled, unsurpassable, unsurpassed, unthinkable, unthought-of,
unusual, unwonted, whole, without equal, without
parallel, wonderful,
wondrous