Dedekind cut
In mathematics, Dedekind cuts, named after German mathematician Richard Dedekind but previously considered by Joseph Bertrand, are а method of construction of the real numbers from the rational numbers. A Dedekind cut is a partition of the rational numbers into two sets A and B, such that all elements of A are less than all elements of B, and A contains no greatest element. The set B may or may not have a smallest element among the rationals. If B has a smallest element among the rationals, the cut corresponds to that rational. Otherwise, that cut defines a unique irrational number which, loosely speaking, fills the "gap" between A and B. In other words, A contains every rational number less than the cut, and B contains every rational number greater than or equal to the cut. An irrational
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Dedekind cut
In mathematics, Dedekind cuts, named after German mathematician Richard Dedekind but previously considered by Joseph Bertrand, are а method of construction of the real numbers from the rational numbers. A Dedekind cut is a partition of the rational numbers into two sets A and B, such that all elements of A are less than all elements of B, and A contains no greatest element. The set B may or may not have a smallest element among the rationals. If B has a smallest element among the rationals, the cut corresponds to that rational. Otherwise, that cut defines a unique irrational number which, loosely speaking, fills the "gap" between A and B. In other words, A contains every rational number less than the cut, and B contains every rational number greater than or equal to the cut. An irrational
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Dedekindův řez je matematický ...... íselného oboru reálných čísel.
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Een dedekindsnede, ook snede v ...... genoemd naar Richard Dedekind.
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Em matemática, cortes de Dedek ...... al que não tem maior elemento.
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En matemàtiques, un tall de De ...... entre» els nombres racionals).
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En mathématiques, une coupure ...... tre » les nombres rationnels).
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In matematica una sezione di D ...... e in ogni punto del continuum.
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In mathematics, Dedekind cuts, ...... nuum without any further gaps.
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Inom matematiken är Dedekindsn ...... mängden av alla Dedekindsnitt.
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Las cortaduras de Dedekind son ...... ción del Análisis Matemático.
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Przekrój Dedekinda – para podz ...... że produkuje ona ten przekrój.
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title
Dedekind cut
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wikiPageUsesTemplate
subject
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Dedekindův řez je matematický ...... íselného oboru reálných čísel.
@cs
Een dedekindsnede, ook snede v ...... genoemd naar Richard Dedekind.
@nl
Em matemática, cortes de Dedek ...... al que não tem maior elemento.
@pt
En matemàtiques, un tall de De ...... entre» els nombres racionals).
@ca
En mathématiques, une coupure ...... tre » les nombres rationnels).
@fr
In matematica una sezione di D ...... dipendente dal detto assioma).
@it
In mathematics, Dedekind cuts, ...... qual to the cut. An irrational
@en
Inom matematiken är Dedekindsn ...... an med snittet av två mängder.
@sv
Las cortaduras de Dedekind son ...... ción del Análisis Matemático.
@es
Przekrój Dedekinda – para podz ...... że produkuje ona ten przekrój.
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Cortes de Dedekind
@es
Cortes de Dedekind
@pt
Coupure de Dedekind
@fr
Dedekind cut
@en
Dedekindscher Schnitt
@de
Dedekindsnede
@nl
Dedekindsnitt
@sv
Dedekindův řez
@cs
Przekrój Dedekinda
@pl
Sezione di Dedekind
@it