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  2. Russell's paradox - Wikipedia

    en.wikipedia.org/wiki/Russell's_paradox

    Let R be the set of all sets that are not members of themselves. (This set is sometimes called "the Russell set".) If R is not a member of itself, then its definition entails that it is a member of itself; yet, if it is a member of itself, then it is not a member of itself, since it is the set of all sets that are not members of themselves. The ...

  3. Lexical set - Wikipedia

    en.wikipedia.org/wiki/Lexical_set

    A lexical set is a group of words that share a particular vowel or consonant sound. A phoneme is a basic unit of sound in a language that can distinguish one word from another. Most commonly, following the work of phonetician John C. Wells, a lexical set is a class of words in a language that share a certain vowel phoneme.

  4. Paradoxes of set theory - Wikipedia

    en.wikipedia.org/wiki/Paradoxes_of_set_theory

    After all this, the version of the "set of all sets" paradox conceived by Bertrand Russell in 1903 led to a serious crisis in set theory. Russell recognized that the statement x = x is true for every set, and thus the set of all sets is defined by {x | x = x}. In 1906 he constructed several paradox sets, the most famous of which is the set of ...

  5. Universal set - Wikipedia

    en.wikipedia.org/wiki/Universal_set

    Russell's paradox concerns the impossibility of a set of sets, whose members are all sets that do not contain themselves. If such a set could exist, it could neither contain itself (because its members all do not contain themselves) nor avoid containing itself (because if it did, it should be included as one of its members). [2]

  6. Element (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Element_(mathematics)

    The expressions "A includes x" and "A contains x" are also used to mean set membership, although some authors use them to mean instead "x is a subset of A". [2] Logician George Boolos strongly urged that "contains" be used for membership only, and "includes" for the subset relation only.

  7. Bag-of-words model - Wikipedia

    en.wikipedia.org/wiki/Bag-of-words_model

    It disregards word order (and thus most of syntax or grammar) but captures multiplicity. The bag-of-words model is commonly used in methods of document classification where, for example, the (frequency of) occurrence of each word is used as a feature for training a classifier. [1] It has also been used for computer vision. [2]

  8. Syntactic Structures - Wikipedia

    en.wikipedia.org/wiki/Syntactic_Structures

    Chomsky uses this argument as well to motivate the establishment of distinct levels of linguistic analysis. [75] Chomsky then shows that a grammar which analyzes sentences up to the phrase structure level contains many constructional homonymities at the phrase structure level where the resulting ambiguities need to be explained at a higher level.

  9. Complement (set theory) - Wikipedia

    en.wikipedia.org/wiki/Complement_(set_theory)

    If A is a set, then the absolute complement of A (or simply the complement of A) is the set of elements not in A (within a larger set that is implicitly defined). In other words, let U be a set that contains all the elements under study; if there is no need to mention U, either because it has been previously specified, or it is obvious and unique, then the absolute complement of A is the ...

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