Therefore, A, B, and C are simply different ways to represent the same set. Ranee Wilhelmy Teacher. What is a famous paradox? Russell's paradox is the most famous of the logical or set-theoretical paradoxes. Emili Horschler Reviewer. What is the most famous paradox? Liar Paradox Epimenides Paradox This is a well known paradox written by the great stoical logician Chrysippos. Crocodile Sophism. Is it possible to give what we don't have? What is better - eternal bliss or a simple bread?
Joselina Arche Reviewer. What is the symbol for a universal set? Vanya Borobio Reviewer. What is the theory of paradox? A paradox , also known as an antinomy, is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion.
Zaher Retola Reviewer. What does N mean in sets? Definition: The number of elements in a set is called the cardinal number, or cardinality, of the set. Find the cardinal number of each set. Ask A Question. Co-authors: 7. Updated On: 13th February, Views: I think part of the answer to Russell's Paradox has to do with the distinction between a set as a collection of things and the "name" of the set.
A set that actually contains itself would be in an infinite regression of things. This is not an unusual confusion, when the name of a thing comes to be a placeholder for the thing itself -- you can play with the symbol and forget that the substance of what it is actually composed of has some reality.
This can work in lists of other symbols, as in the example of catalogues or other such lists that only include references and not actual objects. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group.
Create a free Team What is Teams? Learn more. Example of set which contains itself Ask Question. Asked 8 years, 11 months ago. Active 6 years, 3 months ago. Viewed 22k times. Sign in. Thanks for reading Scientific American.
Create your free account or Sign in to continue. See Subscription Options. Go Paperless with Digital. John T. Get smart. Sign Up. Support science journalism. All of this reminds us that fruitful work can arise from the most unlikely of observations. The Paradox 2. History of the Paradox 3. Early Responses to the Paradox 4. The Paradox Central to any theory of sets is a statement of the conditions under which sets are formed.
Mankind, for example, is not a man. Form now the assemblage of all classes which are not members of themselves. This is a class: is it a member of itself or not? If it is, it is one of those classes that are not members of themselves, i.
If it is not, it is not one of those classes that are not members of themselves, i. Thus of the two hypotheses — that it is, and that it is not, a member of itself — each implies its contradictory. This is a contradiction. History of the Paradox Russell appears to have discovered his paradox in the late spring of , while working on his Principles of Mathematics It was almost superhuman and a telling indication of that of which men are capable if their dedication is to creative work and knowledge instead of cruder efforts to dominate and be known.
Quoted in van Heijenoort , Of course, Russell too was concerned about the consequences of the contradiction. As Whitehead and Russell explain, An analysis of the paradoxes to be avoided shows that they all result from a kind of vicious circle. Bibliography Anderson, C. Anthony, Barwise, Jon, Bealer, George, Beaney, Michael, Cantini, Andrea, Church, Alonzo, a. Irvine, Bertrand Russell: Critical Assessments , vol.
Coffa, Alberto, Copi, Irving, Demopoulos, William, and Peter Clark, Deutsch, Harry, Ebbinghaus, Heinz-Dieter, and Volker Peckhaus, Forster, T. Frege, Gottlob, Gabbay, Dov M. Galaugher, J. Garciadiego, A. Grattan-Guinness, I. Griffin, Nicholas ed. Hallett, Michael, Halmos, Paul R.
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