VS.

# Idea vs. Ideal

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Ideanoun

(philosophy) An abstract archetype of a given thing, compared to which real-life examples are seen as imperfect approximations; pure essence, as opposed to actual examples.

Optimal; being the best possibility.

Ideanoun

(obsolete) The conception of someone or something as representing a perfect example; an ideal.

Perfect, flawless, having no defects.

Ideanoun

(obsolete) The form or shape of something; a quintessential aspect or characteristic.

Pertaining to ideas, or to a given idea.

Ideanoun

An image of an object that is formed in the mind or recalled by the memory.

‘The mere idea of you is enough to excite me.’;

Existing only in the mind; conceptual, imaginary.

Ideanoun

More generally, any result of mental activity; a thought, a notion; a way of thinking.

Teaching or relating to the doctrine of idealism.

‘the ideal theory or philosophy’;

Ideanoun

A conception in the mind of something to be done; a plan for doing something, an intention.

‘I have an idea of how we might escape.’;

(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.’;

Ideanoun

A purposeful aim or goal; intent

‘If you keep sweet-talking her like that, you're going to talk her right out of her pants.’;

Idealnoun

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 - Carl Schurz’;

Ideanoun

A vague or fanciful notion; a feeling or hunch; an impression.

‘He had the wild idea that if he leant forward a little, he might be able to touch the mountain-top.’;

Idealnoun

A subring closed under multiplication by its containing ring.

‘Let $\mathbb\left\{Z\right\}$ be the ring of integers and let $2\mathbb\left\{Z\right\}$ be its ideal of even integers. Then the quotient ring $\mathbb\left\{Z\right\} / 2\mathbb\left\{Z\right\}$ is a Boolean ring.’; ‘The product of two ideals $\mathfrak\left\{a\right\}$ and $\mathfrak\left\{b\right\}$ is an ideal $\mathfrak\left\{a b\right\}$ which is a subset of the intersection of $\mathfrak\left\{a\right\}$ and $\mathfrak\left\{b\right\}$. This should help to understand why maximal ideals are prime ideals. Likewise, the union of $\mathfrak\left\{a\right\}$ and $\mathfrak\left\{b\right\}$ is a subset of $\mathfrak\left\{a + b\right\}$.’;

Ideanoun

(music) A musical theme or melodic subject.

Idealnoun

A non-empty lower set (of a partially ordered set) which is closed under binary suprema (a.k.a. joins).

Ideanoun

The transcript, image, or picture of a visible object, that is formed by the mind; also, a similar image of any object whatever, whether sensible or spiritual.

‘Her sweet idea wandered through his thoughts.’; ‘Being the right idea of your fatherBoth in your form and nobleness of mind.’; ‘This representation or likeness of the object being transmitted from thence [the senses] to the imagination, and lodged there for the view and observation of the pure intellect, is aptly and properly called its idea.’;

Idealnoun

(set theory) A collection of sets, considered small or negligible, such that every subset of each member and the union of any two members are also members of the collection.

‘Formally, an ideal $I$ of a given set $X$ is a nonempty subset of the powerset $\mathcal\left\{P\right\}\left(X\right)$ such that: $\left(1\right)\ \emptyset \in I$, $\left(2\right)\ A \in I \and B \subseteq A\implies B\in I$ and $\left(3\right)\ A,B \in I\implies A\cup B \in I$.’;

Ideanoun

A general notion, or a conception formed by generalization.

‘Alice had not the slightest idea what latitude was.’;

Idealnoun

A Lie subalgebra (subspace that is closed under the Lie bracket) 𝖍 of a given Lie algebra 𝖌 such that the Lie bracket [𝖌,𝖍] is a subset of 𝖍.

Ideanoun

Hence: Any object apprehended, conceived, or thought of, by the mind; a notion, conception, or thought; the real object that is conceived or thought of.

‘Whatsoever the mind perceives in itself, or as the immediate object of perception, thought, or undersanding, that I call idea.’;

Existing in idea or thought; conceptional; intellectual; mental; as, ideal knowledge.

Ideanoun

A belief, option, or doctrine; a characteristic or controlling principle; as, an essential idea; the idea of development.

‘That fellow seems to me to possess but one idea, and that is a wrong one.’; ‘What is now "idea" for us? How infinite the fall of this word, since the time where Milton sang of the Creator contemplating his newly-created world, -"how it showed . . . Answering his great idea," -to its present use, when this person "has an idea that the train has started," and the other "had no idea that the dinner would be so bad!"’;

Reaching an imaginary standard of excellence; fit for a model; faultless; as, ideal beauty.

‘There will always be a wide interval between practical and ideal excellence.’;

Ideanoun

A plan or purpose of action; intention; design.

‘I shortly afterwards set off for that capital, with an idea of undertaking while there the translation of the work.’;

Existing in fancy or imagination only; visionary; unreal.

Ideanoun

A rational conception; the complete conception of an object when thought of in all its essential elements or constituents; the necessary metaphysical or constituent attributes and relations, when conceived in the abstract.

Teaching the doctrine of idealism; as, the ideal theory or philosophy.

Ideanoun

A fiction object or picture created by the imagination; the same when proposed as a pattern to be copied, or a standard to be reached; one of the archetypes or patterns of created things, conceived by the Platonists to have excited objectively from eternity in the mind of the Deity.

‘Thence to behold this new-created world,The addition of his empire, how it showedIn prospect from his throne, how good, how fair,Answering his great idea.’;

Imaginary.

Ideanoun

the content of cognition; the main thing you are thinking about;

‘it was not a good idea’; ‘the thought never entered my mind’;

Idealnoun

A mental conception regarded as a standard of perfection; a model of excellence, beauty, etc.

‘The ideal is to be attained by selecting and assembling in one whole the beauties and perfections which are usually seen in different individuals, excluding everything defective or unseemly, so as to form a type or model of the species. Thus, the Apollo Belvedere is the ideal of the beauty and proportion of the human frame.’;

Ideanoun

a personal view;

‘he has an idea that we don't like him’;

Idealnoun

the idea of something that is perfect; something that one hopes to attain

Ideanoun

an approximate calculation of quantity or degree or worth;

‘an estimate of what it would cost’; ‘a rough idea how long it would take’;

Idealnoun

model of excellence or perfection of a kind; one having no equal

Ideanoun

your intention; what you intend to do;

‘he had in mind to see his old teacher’; ‘the idea of the game is to capture all the pieces’;

conforming to an ultimate standard of perfection or excellence; embodying an ideal

Ideanoun

(music) melodic subject of a musical composition;

‘the theme is announced in the first measures’; ‘the accompanist picked up the idea and elaborated it’;

constituting or existing only in the form of an idea or mental image or conception;

‘a poem or essay may be typical of its period in idea or ideal content’;

Ideanoun

a thought or suggestion as to a possible course of action

‘recently, the idea of linking pay to performance has caught on’; ‘it's a good idea to do some research before you go’;

of or relating to the philosophical doctrine of the reality of ideas

Ideanoun

a mental impression

‘our menu list will give you some idea of how interesting a low-fat diet can be’;

satisfying one's conception of what is perfect; most suitable

‘this is an ideal opportunity to save money’; ‘the swimming pool is ideal for a quick dip’;

Ideanoun

an opinion or belief

existing only in the imagination; desirable or perfect but not likely to become a reality

‘in an ideal world, we might have made a different decision’;

Ideanoun

the aim or purpose

‘I took a job with the idea of getting some money together’;

representing an abstract or hypothetical optimum

‘mathematical modelling can determine theoretically ideal conditions’;

Ideanoun

(in Platonic thought) an eternally existing pattern of which individual things in any class are imperfect copies.

Idealnoun

a person or thing regarded as perfect

‘you're my ideal of how a man should be’;

Ideanoun

(in Kantian thought) a concept of pure reason, not empirically based in experience.

Idealnoun

a standard or principle to be aimed at

‘tolerance and freedom, the liberal ideals’;

Idea

In common usage and in philosophy, ideas are abstract concepts. Also in philosophy, ideas can also be mental representational images of some object.