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A relation p simply orders a set Y iff p F\ (Y X Y) is a simple ordering in Y. The
familiar ordering of the real numbers is a typical example of a simple ordering. In
contrast, inclusion for sets is not. in general. a simple ordering. To point out the ...
A relation R is a strict simple ordering of the set A if and only if R is asymmetric,
transitive, and connected in A. As is to be expected, a strict simple ordering of A is
just a connected strict partial ordering of A. The relation < in the set of numbers is
...
3
Fundamentals of Real Analysis
(iii) x < y & y < x => x = y (antisymmetry). A relation satisfying only (i) and (ii) is
called a pre-ordering of X . Other notations in use for such relations are > , C , D ,-
<,>- , etc. A simple ordering (or total ordering, linear ordering) is a partial ordering
...
Sterling K. Berberian, 1998
Actually, as we shall see, we need assume only that R is connected in A rather
than it is a strict simple ordering of A. The asymmetry and transitivity of R in A are
then provable, as is the fact that any element of A except the last (under thc ...
5
Elements of Advanced Mathematics, Third Edition
A simple ordering is sometimes also called a total ordering. We shall say more
about this topic in Sections 4.5 and 5.2. EXAMPLE 4.2.4 Let S D R;the real
numbers. Let us say that .x;y/ 2 R if y x 0. It is straightforward to verify that
properties (a), ...
6
The Number Systems: Foundations of Algebra and Analysis
The example (3:3—2) shows that the statement that < is a simple ordering of P is
certainly insufficient to characterize it. Before we proceed to finding a correct
characterization, it should be noted that the conditions to be a simple ordering
are ...
7
Continuum Theory: An Introduction
(3) For any*, yeS(p,q) — {p,q},y <sx if and only ifyePx [where P, is as in (1) of 6.12
]. Recall the definitions of the following general notions. 6.14 Definition of Simple
Ordering and Order Topology. A binary relation < for a set Y is called a simple ...
8
The Foundations of Statistics
It is sometimes convenient to supplement the relation 5 by other relations derived
from it in accordance with the definitions in Table 1, analogous definitions being
applicable to any simple ordering. The assumption of simple ordering, Pl, has ...
9
Electronic Journal of Information Systems Evaluation
Ordering medication is simple 8. Dispensing medication is simple 9.
Administering medication is simple Ordering medicationistoo time consuming 10.
Ordering medication is too time consuming Dispensing medication is too time
consuming ...
Delft University of Technology
10
Compositionality in Formal Semantics: Selected Papers by ...
is a DENSE SIMPLE ORDERING OF T if and only if ≤ is a simple ordering of T
and for all t, t′ in T such that t < t′, there exists t′′ in T such that t < t′′ and t
′′ < t′. Montague has given an analysis of the present progressive tense.3
Let ...
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