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Ideal vs Law - What's the difference?

ideal | law |

In mathematics terms the difference between ideal and law

is that ideal is not actually present, but considered as present when limits at infinity are included while law is a statement that is true under specified conditions.

As nouns the difference between ideal and law

is that ideal is (a perfect standard of beauty, intellect etc.)A perfect standard of beauty, intellect etc., or a standard of excellence to aim at while law is the body of rules and standards issued by a government, or to be applied by courts and similar authorities.

As proper nouns the difference between ideal and law

is that ideal is a city in Georgia, USA while Law is {{surname|patronymic|from=given names}.

As an adjective ideal

is optimal; being the best possibility.

As an interjection law is

an exclamation of mild surprise; lawks.

ideal

English

Adjective

(en adjective)
  • Optimal; being the best possibility.
  • Perfect, flawless, having no defects.
  • * Rambler
    • There will always be a wide interval between practical and ideal excellence.
  • Pertaining to ideas, or to a given idea.
  • Existing only in the mind; conceptual, imaginary.
  • * 1796 , Matthew Lewis, The Monk , Folio Society 1985, p. 256:
    • The idea of ghosts is ridiculous in the extreme; and if you continue to be swayed by ideal terrors —
  • * 1818 , , [[s:Frankenstein/Chapter 4, Chapter 4],
    • Life and death appeared to me ideal bounds, which I should first break through, and pour a torrent of light into our dark world.
  • Teaching or relating to the doctrine of idealism.
    • the ideal theory or philosophy
  • (mathematics) Not actually present, but considered as present when limits at infinity are included.
    • ideal point
    An ideal triangle in the hyperbolic disk is one bounded by three geodesics that meet precisely on the circle.

    Synonyms

    * See also

    Related terms

    * ideality * idealless * ideally * idealism * idealistic * idealize

    Noun

    (en noun)
  • A perfect standard of beauty, intellect etc., or a standard of excellence to aim at.
    • Ideals are like stars; you will not succeed in touching them with your hands. But like the seafaring man on the desert of waters, you choose them as your guides, and following them you will reach your destiny -
  • (mathematics, order theory) A non-empty]] lower set (of a partially ordered set) which is [[closure, closed under binary suprema (a.k.a. joins).[http://en.wikipedia.org/wiki/Boolean_prime_ideal_theorem#Prime_ideal_theorems]
    • If (1) the empty set were called a "small" set, and (2) any subset of a "small" set were also a "small" set, and (3) the union of any pair of "small" sets were also a "small" set, then the set of all "small" sets would form an ideal .
  • (for example, algebra) A subring closed under multiplication by its containing ring.
    • Let \mathbb{Z} be the ring of integers and let 2\mathbb{Z} be its ideal of even integers. Then the quotient ring \mathbb{Z} / 2\mathbb{Z} is a Boolean ring.
    The product of two ideals \mathfrak{a} and \mathfrak{b} is an ideal \mathfrak{a b} which is a subset of the intersection of \mathfrak{a} and \mathfrak{b}. This should help to understand why maximal ideals' are prime ' ideals . Likewise, the union of \mathfrak{a} and \mathfrak{b} is a subset of \mathfrak{a + b}.

    Antonyms

    * (order theory) filter

    Derived terms

    * left ideal * right ideal * two-sided ideal * principal ideal

    External links

    * (wikipedia)

    Anagrams

    * ----

    law

    English

    (wikipedia law)

    Etymology 1

    From (etyl) lawe, and gesetnes. More at (l).

    Noun

  • (lb) The body of rules and standards issued by a government, or to be applied by courts and similar authorities.
  • :
  • *, chapter=22
    • , title= The Mirror and the Lamp , passage=Not unnaturally, “Auntie” took this communication in bad part.
  • A particular such rule.
  • :
  • *
  • *:As a political system democracy seems to me extraordinarily foolish,I do not suppose that it matters much in reality whether laws are made by dukes or cornerboys, but I like, as far as possible, to associate with gentlemen in private life.
  • (lb) A written or understood rule that concerns behaviours and their consequences. Laws are usually associated with mores.
  • :
  • A well-established, observed physical characteristic or behavior of nature. The word is used to simply identify "what happens," without implying any explanatory mechanism or causation. Compare to theory.
  • :
  • (lb) A statement that is true under specified conditions.
  • A category of English "common law" petitions that request monetary relief, as opposed to relief in forms other than a monetary judgment; compare to "equity".
  • (lb) One of the official rules of cricket as codified by the MCC.
  • The police.
  • :
  • (lb) One of the two metaphysical forces of the world in some fantasy settings, as opposed to chaos.
  • An oath, as in the presence of a court. See wager of law.
    • Hyponyms
    * sharia law
    Derived terms
    * above the law * against the law * a law unto oneself * * Avogadro’s law * Beer-Lambert law * Boyle’s law * bylaw * canon law * Charles’ law * civil law * common law * contract law * corn laws * Coulomb’s law * criminal law * de Morgan’s laws * employment law * family law * Faraday’s laws * federal law * feudal law * Fourier’s law * Gauss’s law * Graham’s law * Gresham’s law * Henry’s law * Hooke’s law * Hubble’s law * international law * into law * Kepler’s laws of planetary motion * Kerchoff’s laws * law and order * lawful * lawgiver * lawlike * law lord * lawmaker, law-maker * law of cosines * law of large numbers * law of sines * law of small numbers * law of tangents * law of the land * law of the tongue * lay down the law * long arm of the law * lynch law * martial law * Moore’s law * Murphy's law * natural law * Newton’s law of cooling * Newton’s law of gravitation * Newton’s laws of motion * Ohm’s law * physical law * power law * Poiseuille’s law * possession is nine points of the law * property law * Roman law * statuate (statute)+law=statuate law (US) * state law * statute law (Commonwealth English) * Stefan-Boltzmann law * Stokes’ law * sus law * take the law into one’s own hands * the law is an ass * three laws of robotics * unwritten law * Zipf’s law

    See also

    * * *

    Etymology 2

    From (etyl) . Also spelled low.

    Noun

    (en noun)
  • (obsolete) a tumulus of stones
  • a hill
  • * 1892 , Robert Louis Stevenson, Across the Plains
    • You might climb the Law [...] and behold the face of many counties.

    Etymology 3

    Compare (la).

    Interjection

    (en interjection)
  • (dated) An exclamation of mild surprise; lawks.

    • References

    Etymology] in [[:w:da:ODS, ODS]

    Statistics

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    Anagrams

    * ----