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Statements

Subject Item
dbr:Archimedean_group
rdf:type
yago:Abstraction100002137 yago:Group100031264 yago:WikicatOrderedGroups
rdfs:label
Archimedean group Grup Archimedean
rdfs:comment
In abstract algebra, a branch of mathematics, an Archimedean group is a linearly ordered group for which the Archimedean property holds: every two positive group elements are bounded by integer multiples of each other. The set R of real numbers together with the operation of addition and the usual ordering relation between pairs of numbers is an Archimedean group. By a result of Otto Hölder, every Archimedean group is isomorphic to a subgroup of this group. The name "Archimedean" comes from Otto Stolz, who named the Archimedean property after its appearance in the works of Archimedes. Dalam aljabar abstrak, sebuah cabang dari matematika, Grup Archimedean adalah yang sifat Archimedean berlaku: setiap dua elemen grup positif dibatasi oleh kelipatan bilangan bulat satu sama lain. Himpunan R dari bilangan real bersama dengan operasi penjumlahan dan hubungan urutan biasa antara pasangan bilangan adalah grup Archimedean. Dengan hasil dari Otto Hölder, setiap grup Archimedean menjadi subgrup dari grup ini. Nama "Archimedean" berasal dari , yang menamai properti Archimedean setelah kemunculannya dalam karya Archimedes.
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dbr:Surreal_number dbr:Commutative_monoid dbr:Commutative_property dbr:Mathematical_proof dbr:Archimedes dbr:Cyclic_group dbr:Linearly_ordered_group dbr:Hyperreal_number dbr:Hahn_embedding_theorem dbr:Mathematics dbr:Monoid dbr:Group_(mathematics) dbr:Group_isomorphism dbr:Integer dbr:Binary_operation dbr:Dedekind_cut dbr:Linear_order dbr:Otto_Stolz dbr:Subgroup dbr:Finite_group dbr:Non-Archimedean_ordered_field dbr:Lexicographic_order dbr:Dyadic_rational dbr:Inverse_element dbr:Embedding dbr:P-adic_number dbr:Origin_(mathematics) dbr:Even_number dbr:Archimedean_equivalence dbr:Abelian_group dbr:Cartesian_coordinate dbr:Real_number dbr:Associativity dbr:Euclidean_plane dbr:Isomorphic dbr:Non-standard_analysis dbr:Abstract_algebra dbr:Converse_(logic) dbr:Operation_(mathematics) dbr:Natural_number dbr:Archimedean_property dbr:Otto_Hölder dbr:Infinitesimal dbr:Rational_number dbc:Ordered_groups dbr:Identity_element dbr:Pointwise
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Dalam aljabar abstrak, sebuah cabang dari matematika, Grup Archimedean adalah yang sifat Archimedean berlaku: setiap dua elemen grup positif dibatasi oleh kelipatan bilangan bulat satu sama lain. Himpunan R dari bilangan real bersama dengan operasi penjumlahan dan hubungan urutan biasa antara pasangan bilangan adalah grup Archimedean. Dengan hasil dari Otto Hölder, setiap grup Archimedean menjadi subgrup dari grup ini. Nama "Archimedean" berasal dari , yang menamai properti Archimedean setelah kemunculannya dalam karya Archimedes. In abstract algebra, a branch of mathematics, an Archimedean group is a linearly ordered group for which the Archimedean property holds: every two positive group elements are bounded by integer multiples of each other. The set R of real numbers together with the operation of addition and the usual ordering relation between pairs of numbers is an Archimedean group. By a result of Otto Hölder, every Archimedean group is isomorphic to a subgroup of this group. The name "Archimedean" comes from Otto Stolz, who named the Archimedean property after its appearance in the works of Archimedes.
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wikipedia-en:Archimedean_group