Ideal vs Chimerical - What's the difference?

ideal | chimerical | Related terms |

Ideal is a related term of chimerical.

As a noun ideal

is ideal (perfect standard).

As an adjective chimerical is

of or pertaining to a chimera.

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

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

* ----

chimerical

English

Adjective

(en adjective)

Of or pertaining to a chimera.

Being a figment of the imagination; fantastic (in the archaic sense).

* 1877 ,

"Yes; I have a turn both for observation and for deduction. The theories which I have expressed there, and which appear to you to be so chimerical , are really extremely practical—so practical that I depend upon them for my bread and cheese."

a chimerical goal

Inherently fantastic; wildly fanciful.

Resulting from the expression of two or more genes that originally coded for separate proteins.

Derived terms

* chimerically