Noncomputability, math, Marketing Management

Theory of Noncomputability, Define Noncomputability

When we want to specify the elements of a set that contains only a few elements, the most direct and obvious way is to exhaustively list all the elements in the set. However, when a set contains a large number of an infinite number of elements, exhaustively listing all elements in the set becomes impractical or impossible. For example, we may have

P = {x|x is a high school student in Illinios}

Where P is a finite set with a large number of elements. We may have,

Q = {x|x is a perfect square}

Where Q is a countably infinite set of integers. Also, we may have,

R = {x| {a, b} ⊆ x}

Note that R is a set of sets such that every element in R has the set {a, b} as a subset.

We want to show that there is a possible pitfall when we specify the elements of a set by specifying the properties that uniquely characterize these elements.

Consider the set

S = {x|x ∉ x}

It seems that we have followed the "recipe" and have defined a set S such that a set x is an element of S ifx ∉ x. Thus for example, {a, b} is an element of S because {a, b} ∉ {a, b}. {{a}} is also an element of S because {{a}} ∉ {{a}}. However, suppose someone wants to know whether S is an element of S. In other words, she wants to know whether S ? S. Following the specification, we say that for S to be an element of S it must be the case that S ∉ S, which is a self contradictory statement. Let us turn around and assume that S is not an element of S; that is S ∉ S. Then, according to the specification, S should be an element of S. That is, if S ∉ S then S ? S- again, a self-contradictory statement. We hasten to point out that what we have said is not just a pun and have by no means attempted to confuse the reader with entangled and complicated syntax. Rather, contrary to our intuition, it is not always the case that we can precisely specify the elements of a set by specifying the properties of the elements in the set. Such an observation was first made by B. Russell in 1911, and is referred to as Russell's appendix. 

Posted Date: 2/15/2012 7:52:29 AM | Location : United States







Related Discussions:- Noncomputability, math, Assignment Help, Ask Question on Noncomputability, math, Get Answer, Expert's Help, Noncomputability, math Discussions

Write discussion on Noncomputability, math
Your posts are moderated
Related Questions
.explain Henry Assael Model of buying decision behaviour along with diagram.

What is Concept Testing Strategy Development? Concept Testing: To estimate ideas properly. This may be essential to test product concepts testing is a phase in that a sma

Explain about the Professional and Direct Purchasing in business market and the consumer market. Professional Purchasing: Products into business markets are purchased usua


New Product Development Organizations have to develop new services and products. A company must be good at making new products. It also ought to manage them in the face of mod

The problem formulation are: R the set of all mesh routers N number of mesh routers K the maximum

What are Industrial Goods? Industrial Goods: Industrial goods are divided in five categories further. These goods are not directly utilized by consumers: installations, a

a side of a square is represented by x-3.what expression represents the area of the square?

Question 1: i). Use appropriate examples to describe and elaborate on the "Functions of advertising". ii) There are different types of advertising like Retail Advertising,

Explain about the product assortment in briefly. “A product mix (also termed as product assortment) is the set of all products and items which a particular sellers offers for s