The difference between Ideal and Model
When used as nouns, ideal means a perfect standard of beauty, intellect etc., or a standard of excellence to aim at, whereas model means a person who serves as a subject for artwork or fashion, usually in the medium of photography but also for painting or drawing.
When used as adjectives, ideal means optimal, whereas model means worthy of being a model.
Model is also verb with the meaning: to display for others to see, especially in regard to wearing clothing while performing the role of a fashion model.
check bellow for the other definitions of Ideal and Model
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Ideal as an adjective:
Optimal; being the best possibility.
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Ideal as an adjective:
Perfect, flawless, having no defects.
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Ideal as an adjective:
Pertaining to ideas, or to a given idea.
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Ideal as an adjective:
Existing only in the mind; conceptual, imaginary.
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Ideal as an adjective:
Teaching or relating to the doctrine of idealism.
Examples:
"the ideal theory or philosophy"
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Ideal as an adjective (mathematics):
Not actually present, but considered as present when limits at infinity are included.
Examples:
"'ideal point"
"An ideal triangle in the hyperbolic disk is one bounded by three geodesics that meet precisely on the circle."
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Ideal as a noun:
A perfect standard of beauty, intellect etc., or a standard of excellence to aim at.
Examples:
"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'' - [[w:Carl Schurz Carl Schurz]]"
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Ideal as a noun (algebra, ring theory):
A subring closed under multiplication by its containing ring.
Examples:
"Let <math>\mathbb{Z}</math> be the ring of integers and let <math>2\mathbb{Z}</math> be its ideal of even integers. Then the quotient ring <math>\mathbb{Z} / 2\mathbb{Z}</math> is a Boolean ring."
"The product of two ideals <math>\mathfrak{a}</math> and <math>\mathfrak{b}</math> is an ideal <math>\mathfrak{a b}</math> which is a subset of the intersection of <math>\mathfrak{a}</math> and <math>\mathfrak{b}</math>. This should help to understand why maximal ideals are prime ideals. Likewise, the union of <math>\mathfrak{a}</math> and <math>\mathfrak{b}</math> is a subset of <math>\mathfrak{a + b}</math>."
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Ideal as a noun (algebra, order theory, lattice theory):
A non-empty lower set (of a partially ordered set) which is closed under binary suprema (a.k.a. joins).
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Ideal as a noun (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.
Examples:
"Formally, an ideal <math>I</math> of a given set <math>X</math> is a nonempty subset of the [[powerset]] <math>\mathcal{P}(X)</math> such that: <math>(1)\ \emptyset \in I</math>, <math>(2)\ A \in I \and B \subseteq A\implies B\in I</math> and <math>(3)\ A,B \in I\implies A\cup B \in I</math>."
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Ideal as a noun (algebra, Lie theory):
A Lie subalgebra (subspace that is closed under the Lie bracket) ๐ of a given Lie algebra ๐ such that the Lie bracket [๐,๐] is a subset of ๐.
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Model as a noun:
A person who serves as a subject for artwork or fashion, usually in the medium of photography but also for painting or drawing.
Examples:
"The beautiful model had her face on the cover of almost every fashion magazine imaginable."
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Model as a noun:
A person, usually an attractive female, hired to show items or goods to the public, such as items given away as prizes on a TV game show.
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Model as a noun:
A representation of a physical object, usually in miniature.
Examples:
"The boy played with a model of a World War II fighter plane."
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Model as a noun:
A simplified representation used to explain the workings of a real world system or event.
Examples:
"The computer weather model did not correctly predict the path of the hurricane."
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Model as a noun:
A style, type, or design.
Examples:
"He decided to buy the turbo engine model of the sports car."
"This year's model features four doors instead of two."
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Model as a noun:
The structural design of a complex system.
Examples:
"The team developed a sound business model."
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Model as a noun:
A successful example to be copied, with or without modifications.
Examples:
"He was a model of eloquence and virtue."
"British parliamentary democracy was seen as a model for other countries to follow."
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Model as a noun (logic):
An interpretation function which assigns a truth value to each atomic proposition.
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Model as a noun (logic):
An interpretation which makes a certain sentence true, in which case that interpretation is called a model of that sentence.
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Model as a noun (manufacturing):
An identifier of a product given by its manufacturer (also called model number).
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Model as a noun (medicine):
An animal that is used to study a human disease or pathology.
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Model as a noun:
Any copy, or resemblance, more or less exact.
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Model as a noun (software architecture):
In software applications using the model-view-controller design pattern, the part or parts of the application that manage the data.
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Model as an adjective:
Worthy of being a model; exemplary.
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Model as a verb (transitive):
To display for others to see, especially in regard to wearing clothing while performing the role of a fashion model.
Examples:
"She modelled the shoes for her friends to see."
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Model as a verb (transitive):
To use as an object in the creation of a forecast or model.
Examples:
"They modelled the data with a computer to analyze the experimentโs results."
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Model as a verb (transitive):
To make a miniature model of.
Examples:
"He takes great pride in his skill at modeling airplanes."
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Model as a verb (transitive):
To create from a substance such as clay.
Examples:
"The sculptor modelled the clay into the form of a dolphin."
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Model as a verb (intransitive):
To make a model or models.
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Model as a verb (intransitive):
To be a model of any kind.
Examples:
"The actress used to model before being discovered by Hollywood."