Ordered Sets, Cardinals, Integers

Nicolas Bourbaki

Chapter Chapter III in Theory of Sets, 2004, pp 131-257 from Springer

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 $$\left( {R\left\{ {x,\left. y \right\}} \right.{\text{ and }}R\left\{ {y,\left. z \right\}} \right.} \right) \Rightarrow R\left\{ {x,\left. z \right\}} \right.,$$ $$\left( {R\left\{ {x,\left. y \right\}} \right.{\text{ and }}R\left\{ {y,\left. x \right\}} \right.} \right) \Rightarrow R\left\{ {x = \left. y \right\}} \right.,$$ $$R\left\{ {x,\left. y \right\}} \right. \Rightarrow \left( {R\left\{ {x,\left. x \right\}} \right.\,\,and\,R\left\{ {y,\left. y \right\}} \right.} \right).$$

Keywords: Order Relation; Canonical Mapping; Finite Subset; Inverse Limit; Great Element (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/978-3-642-59309-3_4

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