BourbakiV1, Istex, Corpus, bibRecord, 001612

Ordered Sets, Cardinals, Integers

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Ordered Sets, Cardinals, Integers

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RBID : ISTEX:6C08EAE32239B3DB1BFCDB376EE52AA39EE35970

Abstract

Abstract: Let R {x,y} be a relation, x and y being distinct letters. R is said to be an order relation with respect to the letters x and y (or between x and y) if $$\left( {R\left\{ {x,\left. y \right\}} \right.{\text{ and }}R\left\{ {y,\left. z \right\}} \right.} \right) \Rightarrow R\left\{ {x,\left. z \right\}} \right.,$$ $$\left( {R\left\{ {x,\left. y \right\}} \right.{\text{ and }}R\left\{ {y,\left. x \right\}} \right.} \right) \Rightarrow R\left\{ {x = \left. y \right\}} \right.,$$ $$R\left\{ {x,\left. y \right\}} \right. \Rightarrow \left( {R\left\{ {x,\left. x \right\}} \right.\,\,and\,R\left\{ {y,\left. y \right\}} \right.} \right).$$

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DOI: 10.1007/978-3-642-59309-3_4

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<front><div type="abstract" xml:lang="en">Abstract: Let R {x,y} be a relation, x and y being distinct letters. R is said to be an order relation with respect to the letters x and y (or between x and y) if $$\left( {R\left\{ {x,\left. y \right\}} \right.{\text{ and }}R\left\{ {y,\left. z \right\}} \right.} \right) \Rightarrow R\left\{ {x,\left. z \right\}} \right.,$$ $$\left( {R\left\{ {x,\left. y \right\}} \right.{\text{ and }}R\left\{ {y,\left. x \right\}} \right.} \right) \Rightarrow R\left\{ {x = \left. y \right\}} \right.,$$ $$R\left\{ {x,\left. y \right\}} \right. \Rightarrow \left( {R\left\{ {x,\left. x \right\}} \right.\,\,and\,R\left\{ {y,\left. y \right\}} \right.} \right).$$</div>
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Ordered Sets, Cardinals, Integers

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