Complement vs Ultrafilter - What's the difference?

complement | ultrafilter |


As nouns the difference between complement and ultrafilter

is that complement is complement, thing added that makes a whole while ultrafilter is a proper filter which has a law of dichotomy for complements.

complement

Noun

(en noun)
  • *:
  • perform all those works of mercy, which Clemens Alexandrinus calls amoris et amicitiæ impletionem et extentionem , the extent and complement of love.
  • (obsolete) The act of completing something, or the fact of being complete; completion, completeness, fulfilment.
  • * 1590 , (Edmund Spenser), The Faerie Queene , III.5:
  • And both encreast the prayse of woman kynde, / And both encreast her beautie excellent: / So all did make in her a perfect complement .
  • The totality, the full amount or number which completes something.
  • * 1851 , (Herman Melville), Moby-Dick :
  • Queequeg sought a passage to Christian lands. But the ship, having her full complement of seamen, spurned his suit; and not all the King his father's influence could prevail.
  • * 2009 , The Guardian , 30 October:
  • Some 11 members of Somerton council's complement of 15 stepped down on Tuesday.
  • (obsolete) Something which completes one's equipment, dress etc.; an accessory.
  • * 1591 , (Edmund Spenser), “The Teares of the Muses [The Tears of the Muses]: Polyhymnia”:
  • *:A doleful case desires a doleful song,
  • *:Without vain art or curious complements.
  • *c. 1599 , (William Shakespeare), , Act 2, Scene 2:
  • *:Garnish'd and deck'd in modest complement,
  • *, I.42:
  • *:A man should be judged by himselfe, and not by his complements .
  • (nautical) The whole working force of a vessel.
  • (heraldry) Fullness (of the moon).
  • * 1912 , Allen Phoebe, Peeps at Heraldry , p.33:
  • The sixth Bishop of Ely had very curious arms, for he bore both sun and moon on his shield, the sun "in his splendour" and the moon "in her complement ".
  • (astronomy, geometry) An angle which, together with a given angle, makes a right angle.
  • Something which completes, something which combines with something else to make up a complete whole; loosely, something perceived to be a harmonious or desirable partner or addition.
  • * Sir J. Stephen
  • History is the complement of poetry.
  • * 2009 , The Guardian , 13 December:
  • London's Kings Place, now one year old, established itself as a venue for imaginative programming, a complement to the evergreen Wigmore Hall.
  • (grammar) A word or group of words that completes a grammatical construction in the predicate and that describes or is identified with the subject or object.
  • *
  • Why has our grammar broken down at this point? It is not difficult to see why. For, we have failed to make any provision for the fact that only some'' Verbs in English (i.e. Verbs like those italicized in (5) (a), traditionally called ''Transitive Verbs'') subcategorize ( = ‘take?) an immediately following NP Complement , whereas others (such as those italicised in (5) (b), traditionally referred to as ''Intransitive Verbs ) do not.
  • (music) An interval which, together with the given interval, makes an octave.
  • (optics) The color which, when mixed with the given color, gives black (for mixing pigments) or white (for mixing light).
  • The complement of blue is orange.
  • (set theory) Given two sets, the set containing one set's elements that are not members of the other set (whether a relative complement or an absolute complement).
  • The complement of the odd numbers is the even numbers, relative to the natural numbers.
  • (immunology) One of several blood proteins that work with antibodies during an immune response.
  • (logic) An expression related to some other expression such that it is true under the same conditions that make other false, and vice versa.
  • (electronics) A voltage level with the opposite logical sense to the given one.
  • (computing) A bit with the opposite value to the given one; the logical complement of a number.
  • (computing, mathematics) The diminished radix complement of a number; the nines' complement of a decimal number; the ones' complement of a binary number.
  • The complement of 01100101_2 is 10011010_2.
  • (computing, mathematics) The radix complement of a number; the two's complement of a binary number.
  • The complement of 01100101_2 is 10011011_2.
  • (computing, mathematics) The numeric complement of a number.
  • The complement of -123 is 123.
  • (genetics) A nucleotide sequence in which each base is replaced by the complementary base of the given sequence: adenine (A) by thymine (T) or uracil (U), cytosine (C) by guanine (G), and vice versa.
  • A DNA molecule is formed from two strands, each of which is the complement of the other.
  • (Shakespeare)

    Verb

    (en verb)
  • To complete, to bring to perfection, to make whole.
  • We believe your addition will complement the team.
  • To provide what the partner lacks and lack what the partner provides.
  • The flavors of the pepper and garlic complement each other, giving a very rich taste in combination.
    I believe our talents really complement each other.
  • To change a voltage, number, color, etc. to its complement.
  • See also

    * compliment * invert * inversion * negate * negation * supplement

    References

    * DeLone et. al. (Eds.) (1975). Aspects of Twentieth-Century Music . Englewood Cliffs, New Jersey: Prentice-Hall. ISBN 0130493465.

    ultrafilter

    English

    Noun

    (en noun)
  • A proper filter which has a law of dichotomy for complements.
  • A proper filter of a set has these three properties: (1) it does not contain the empty set, (2) if it contains a subset then it contains all supersets of that subset, and (3) if it contains a pair of subsets then it also contains their intersection. To make it into an ultrafilter''' it must be made as large as possible without including the empty set. That can be prevented by not allowing any pair of disjoint sets to be both included. If, given a pair of complementary subsets, one of them is prevented from being included, then all subsets of it should be prevented from being included as well, by the second rule. That takes care of all subsets disjoint from the other complementary subset, which should then be included, in order to make the filter approach maximality, i.e., turn it into an '''ultrafilter .
  • (mathematics, order theory) A filter (subset of a poset) that is maximal as a set with respect to the definition of (proper) (term).
  • An ultrafilter is maximal in the sense that if any other element of the poset not already in it were added to it, one could deduce (from the laws which define the filter, and the given ordering relation, i.e., the structure of the poset) that the resulting filter must be improper; i.e., it must contain all the elements of the poset.

    Holonyms

    * poset

    Hypernyms

    * filter

    Hyponyms

    * free ultrafilter * principal ultrafilter