|
Infinite set - Wikipedia, the free encyclopedia
In set theory, an infinite set is a set that is not a finite set. Infinite sets may be countable or uncountable. Some examples are: • the set of all integers, {..., -1, 0, 1, 2, ...}, is a countably...
en.wikipedia.org/wiki/Infinite_set |
|
|||
|
|||
|
|||
|
We will use the following sets based on numbers and prime numbers. ... Next we take a key step: to define equivalence in such a way that it also works for infinite sets. Think of two finite equivalent sets S and T as being ordered. Thus they each have a first, second, third, and so on element.
|
|||
|
We will soon see that there are infinite sets larger than the set of natural numbers (Theorem 3 below), and for them no such sequences can be constructed. However, for cardinalities of that magnitude, most of our proofs will show the absence or failure, rather than the presence, of one-to-one correspondence.
|
|||
|
CiteSeerX - Document Details (Isaac Councill, Lee Giles): It is suggested that there are infinite computable sets of natural numbers with the property that no infinite subset can be computed more simply or more quickly than the whole set. ... 396 An introduction to the theory of numbers – Hardy, ... 13 Retraceable sets – Dekker,
|
|||
|
It is suggested that there are infinite computable sets of natural numbers with the property that no infinite subset can be computed more simply or more quickly than the whole set. Attempts to establish this without restricting in any way the computer involved in the calculations are not G. J. Chait ... Rate this article:
|
|||
|
rdfs:label On the Simplicity and Speed of Programs for Computing Infinite Sets of Natural Numbers. (xsd:string) ... swrc:pages 407-422 (xsd:string)
|
|||
|
Please see the attached file for the fully formatted. ... Sets, One-to-one Correspondence, Infinite Sets and Cardinal Numbers are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.
|
Copyright © 2009, Dictionary.com, LLC. All rights reserved.
Related Topics
