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None of the quantifiers previously discussed apply to a quantification such as There are many integers n < 100, such that n is divisible by 2 or 3 or 5. One possible interpretation mechanism can be obtained as follows: Suppose that in addition to a semantic domain X, we have given a probability measure P defined on X and cutoff numbers 0 < a ...
3 Small number of something Quartet: 4 Referring to people working or collaborating especially in musical performance Great gross: 1,728 A dozen gross (12x144) Hat-trick: 3 The achievement of, a generally positive feat, three times in a game, or another achievement based on the number three [6] Several: 3+ Three or more but not many. Small ...
Sentences without any logical connectives or quantifiers in them are known as atomic sentences; by analogy to atomic formula. Sentences are then built up out of atomic sentences by applying connectives and quantifiers. A set of sentences is called a theory; thus, individual sentences may be called theorems.
A. 2 + 6 + 6 = 14 B. 3 + 3 + 8 = 14. In case 'A', there is no 'eldest child': two children are aged six (although one could be a few minutes or around 9 to 12 months older and they still both be 6). Therefore, when told that one child is the eldest, the census-taker concludes that the correct solution is 'B'. [3]
In mathematics and logic, the term "uniqueness" refers to the property of being the one and only object satisfying a certain condition. [1] This sort of quantification is known as uniqueness quantification or unique existential quantification, and is often denoted with the symbols "∃!" [2] or "∃ =1". For example, the formal statement
is false, because if n is substituted with, for instance, 1, the statement "2·1 > 2 + 1" is false. It is immaterial that "2·n > 2 + n" is true for most natural numbers n: even the existence of a single counterexample is enough to prove the universal quantification false. On the other hand, for all composite numbers n, one has 2·n > 2 + n is ...
Then, "there are exactly 2 things such that φ" is true in A iff the set of things that are such that φ is a member of the set of all subsets of dom(A) of size 2. A Lindström quantifier is a polyadic generalized quantifier, so instead being a relation between subsets of the domain, it is a relation between relations defined on the domain.
In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least one", or "for some". It is usually denoted by the logical operator symbol ∃, which, when used together with a predicate variable, is called an existential quantifier (" ∃x" or "∃(x)" or ...