A subring closed under multiplication by its containing ring.
A subsemigroup with the property that if any semigroup element outside of it is added to any one of its members, the result must lie outside of it.
A non-empty lower set (of a partially ordered set) which is closed under binary suprema (a.k.a. joins).
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.
A perfect standard of beauty, intellect etc., or a standard of excellence to aim at.
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.
Not actually present, but considered as present when limits at infinity are included.
Optimal; being the best possibility.
Existing only in the mind; conceptual, imaginary.
Pertaining to ideas, or to a given idea.
Perfect, flawless, having no defects.
Teaching or relating to the doctrine of idealism.
The neutral element with respect to multiplication in a ring.
One run scored by hitting the ball and running between the wickets; a single.
A joke or amusing anecdote.
A particularly special or compatible person or thing.
A one-dollar bill.
Used instead of ! to amplify an exclamation, parodying unskilled typists who forget to press the shift key while typing exclamation points, thus typing "1".
One o'clock, either a.m. or p.m.
The digit or figure 1.
The first mentioned of two things or people, as opposed to the other.
Functions as a relative pronoun at the end of a relative clause.
Any person (applying to people in general).
One thing (among a group of others); one member of a group.
Any person, entity or thing.
Used as a noun substituent following a possessive determiner.
To cause to become one; to gather into a single whole; to unite.
Whole, entire.
Being an unknown person with the specified name; see also "a certain".
The same.
In agreement.
Being a preeminent example.
Sole, only.
Being a single, unspecified thing; a; any.
Of a period of time, being particular.
Used to emphasize or explain something, with an implied antecedent.
Used at the end of a sentence to highlight the characteristics of someone or something.
A nominalizer; used to form a noun phrase without a head noun.
The cardinality of the smallest nonempty set.
The first positive number in the set of natural numbers.
The number represented by the Arabic numeral 1; the numerical value equal to that cardinal number.
The ordinality of an element which has no predecessor, usually called first or number one.