The difference between Identity element and Unit
When used as nouns, identity element means an element of an algebraic structure which when applied, in either order, to any other element via a binary operation yields the other element, whereas unit means oneness, singularity, seen as a component of a whole number.
Unit is also adjective with the meaning: for each unit.
check bellow for the other definitions of Identity element and Unit
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Identity element as a noun (algebra):
An element of an algebraic structure which when applied, in either order, to any other element via a binary operation yields the other element.
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Unit as a noun (mathematics):
Oneness, singularity, seen as a component of a whole number; a magnitude of one.
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Unit as a noun (sciences):
A standard measure of a quantity.
Examples:
"The centimetre is a unit of length."
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Unit as a noun:
The number one.
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Unit as a noun:
Examples:
"This pill provides 500 units of Vitamin E."
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Unit as a noun:
An organized group comprising people and/or equipment.
Examples:
"He was a member of a special police unit."
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Unit as a noun (military, informal):
A member of a military organization.
Examples:
"The fifth tank brigade moved in with 20 units.'' (''i.e., 20 tanks'')"
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Unit as a noun (US, military):
Any military element whose structure is prescribed by competent authority, such as a table of organization and equipment; specifically, part of an organization.
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Unit as a noun (US, military):
An organization title of a subdivision of a group in a task force.
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Unit as a noun (US, military):
A standard or basic quantity into which an item of supply is divided, issued or detailed. In this meaning, also called unit of issue.
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Unit as a noun (US, military):
With regard to Reserve Components of the Armed Forces, denotes a Selected Reserve unit organized, equipped, and trained for mobilization to serve on active duty as a unit or to augment or be augmented by another unit. Headquarters and support functions without wartime missions are not considered units.
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Unit as a noun (algebra):
The identity element, neutral element.
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Unit as a noun (algebra):
An element having an inverse, an invertible element; an associate of the unity.
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Unit as a noun (category theory):
In an adjunction, a natural transformation from the identity functor of the domain of the left adjoint functor to the composition of the right adjoint functor with the left adjoint functor.
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Unit as a noun (geology):
A volume of rock or ice of identifiable origin and age range that is defined by the distinctive and dominant, easily mapped and recognizable petrographic, lithologic or paleontologic features (facies) that characterize it.
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Unit as a noun (commerce):
An item which may be sold singly.
Examples:
"We shipped nearly twice as many units this month as last month."
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Unit as a noun (UK):
A unit of alcohol.
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Unit as a noun (UK, electricity):
One kilowatt-hour (as recorded on an electricity meter).
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Unit as a noun (Australia, New Zealand):
a measure of housing equivalent to the living quarters of one household, an apartment where a group of apartments is contained in one or more multi-storied buildings or a group of dwellings is in one or more single storey buildings, usually arranged around a driveway.
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Unit as a noun (historical):
A gold coin of the reign of James I, worth twenty shillings.
Examples:
"rfquotek Camden"
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Unit as a noun:
A work unit.
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Unit as a noun (UK, slang):
A physically large person.
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Unit as an adjective:
For each unit.
Examples:
"We have to keep our unit costs down if we want to make a profit."
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Unit as an adjective (mathematics):
Having a size or magnitude of one.