Linear continuum
In the mathematical field of order theory, a continuum or linear continuum is a generalization of the real line. Formally, a linear continuum is a linearly ordered set S of more than one element that is densely ordered, i.e., between any two distinct elements there is another (and hence infinitely many others), and complete, i.e., which "lacks gaps" in the sense that every nonempty subset with an upper bound has a least upper bound. More symbolically: 1.
* S has the least upper bound property, and 2.
* For each x in S and each y in S with x < y, there exists z in S such that x < z < y
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Applied element methodBounded variationCantor–Dedekind axiomCompact spaceConsistency modelContinuumContinuum (order theory)Continuum (topology)Dedekind cutDegeneracy (mathematics)Ham sandwich theoremLeast-upper-bound propertyList of continuity-related mathematical topicsOrder topologyPhononPhysical paradoxReal lineSurreal numberTarski's axiomatization of the reals
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Linear continuum
In the mathematical field of order theory, a continuum or linear continuum is a generalization of the real line. Formally, a linear continuum is a linearly ordered set S of more than one element that is densely ordered, i.e., between any two distinct elements there is another (and hence infinitely many others), and complete, i.e., which "lacks gaps" in the sense that every nonempty subset with an upper bound has a least upper bound. More symbolically: 1.
* S has the least upper bound property, and 2.
* For each x in S and each y in S with x < y, there exists z in S such that x < z < y
has abstract
In matematica, la parola conti ...... uni sottocontinui) non banali.
@it
In the mathematical field of o ...... nterval is a linear continuum.
@en
Kontinuum är den ordnade mängd ...... som t.ex. de naturliga talen.
@sv
No campo matemático da teoria ...... ma generalização da reta real.
@pt
في المجال الرياضي لـ نظرية الت ...... لترتيب الطوبولوجي متصلة أم لا.
@ar
数学の順序理論の分野において、線型連続体(せんけいれんぞくた ...... 使われる点で、線型連続体は特にトポロジーの分野で重要である。
@ja
순서론에서, 선형 연속체(線型連續體, 영어: linear continuum)는 상한이 존재하는 조밀 전순서 집합이다.
@ko
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comment
In matematica, la parola conti ...... al di fuori della retta reale.
@it
In the mathematical field of o ...... sts z in S such that x < z < y
@en
Kontinuum är den ordnade mängd ...... som t.ex. de naturliga talen.
@sv
No campo matemático da teoria ...... ma generalização da reta real.
@pt
في المجال الرياضي لـ نظرية الت ...... يوجد z في S بحيث إن x < z < y
@ar
数学の順序理論の分野において、線型連続体(せんけいれんぞくた ...... 使われる点で、線型連続体は特にトポロジーの分野で重要である。
@ja
순서론에서, 선형 연속체(線型連續體, 영어: linear continuum)는 상한이 존재하는 조밀 전순서 집합이다.
@ko
label
Continuo
@it
Contínuo linear
@pt
Kontinuum (matematik)
@sv
Linear continuum
@en
تسلسل خطي
@ar
線型連続体
@ja
선형 연속체
@ko