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Computer Arithmetic and Validity
book

Computer Arithmetic and Validity

by Ulrich Kulisch
April 2013
Intermediate to advanced content levelIntermediate to advanced
456 pages
16h 7m
English
De Gruyter
Content preview from Computer Arithmetic and Validity
18 Chapter 1 First concepts
1.2 Complete lattices and complete subnets
We begin our discussion of lattices with the following definition.
Definition 1.7. Let fM , g be an ordered set. Then
(O5) M is called a lattice if for any two elements a, b 2 M ,theinffa, bg and the
supfa, bg exist;
(O6) M is called conditionally complete if for every nonempty, bounded subset S
M ,theinfS and the sup S exist;
(O7) M is called completely ordered or a complete lattice if every subset S M
has an infimum and a supremum.
Every finite subset S Dfa
1
, a
2
, :::, a
n
g of a lattice has an infimum and a supre-
mum. We prove this statement by induction. By definition any subset
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Publisher Resources

ISBN: 9783110301731