10 ENGLISH BOOKS RELATING TO «DEDEKIND CUT»
Discover the use of
Dedekind cut in the following bibliographical selection. Books relating to
Dedekind cut and brief extracts from same to provide context of its use in English literature.
1
Foundations and Fundamental Concepts of Mathematics
An example of a Dedekind cut of type (a) is the cut (A l B) in which A consists of
all the rational numbers less than or equal to 2, while B contains all the remaining
rational numbers. Here A has a largest element — namely, 2 — and B has no ...
Howard Whitley Eves, 1997
2
Essays on the Theory of Numbers
This volume contains the two most important essays on the logical foundations of the number system by the famous German mathematician J. W. R. Dedekind.
3
Elementary Analysis: The Theory of Calculus
Thus if a is a Dedekind out, there is a Dedekind cut —a such that a + (—a) I 0*.
How would you define —a? 6.4 Let or and 6 be Dedekind cuts and define the “
product”: 04-6 I {7'17'2 : r1 G a and r2 G (a) Calculate some “products” of
Dedekind ...
4
What is Mathematics, Really?
I'll be satisfied to show that one particular irrational is included as a Dedekind cut
— V 2 . To do so, I must identify a left half-line and right half-line associated with
V 2 . What rationals are less than V 2 ? Certainly all the negative ones, and also ...
5
Foundations of Analysis
In this case, r is called the cut number for the Dedekind cut. Are there Dedekind
cuts that are not determined in this way? Cuts that have no rational cut number?
Example 1.4.2. Describe a Dedekind cut that is not of the form Lr for a rational ...
6
Classical Mathematical Logic: The Semantic Foundations of Logic
The book provides detailed explanations of all proofs and the insights behind the proofs, as well as detailed and nontrivial examples and problems. The book has more than 550 exercises.
7
The Real Numbers and Real Analysis
... G B such that d G Q — A, and a similar argument shows that A C we omit the
details. □ Lemma 1.6.7. Let A be a non-empty family of subsets of Q. Suppose
that X is a Dedekind cut for allX G A. Tjf [JxeA^ 7^ Q> f^en UxeA^ J's a Dedekind
cut.
8
Deleuze and the History of Mathematics: In Defense of the 'New'
The specific developments that Bergson implicitly draws upon are the concept of
multiplicity developed by Bernhard Riemann (b. 1826-1866) in 1854, published
in 1868 (Riemann 1963), and the idea of the Dedekind cut advanced by Richard
...
9
Set Theory and Related Topics
Solution : (i) (L, U) is a Dedekind's cut. This section corresponds to the irrational
number V3. (ii) U= {xGQ:x>0, x2>3}, L = {xEQ:x£U}. It means that all the negative
rational numbers and all the positive rationals whose square is less than 3, ...
10
The Philosophy of Information
Intuitively, a Dedekind cut is a partition of the set of rational numbers into two non
-empty subsets, in such a way as to uniquely define a real number. Following
Dedekind's geometrical description,13 Michael's sword could not be sharper: it
has ...
NEWS ITEMS WHICH INCLUDE THE TERM «DEDEKIND CUT»
Find out what the national and international press are talking about and how the term
Dedekind cut is used in the context of the following news items.
How dialectical materialism contributes to the understanding of the …
... dialectical thought in mathematics is given by the German mathematician Richard Dedekind in what has become known as the Dedekind cut. «Political Affairs Magazine, Jan 14»
