Russell's Antinomy
Let 
be the set of all sets which are not members of themselves. Then is neither a member of itself nor not a memberof itself. Symbolically, let 
. Then 
Iff 
.
Bertrand Russell discovered this Paradox and sent it in a letter to G. Frege just as Frege was completing Grundlagen der Arithmetik. This invalidated much of the rigor of the work, and Frege was forced to add a note at the endstating, ``A scientist can hardly meet with anything more undesirable than to have the foundation give way just as the workis finished. I was put in this position by a letter from Mr. Bertrand Russell when the work was nearly through thepress.''
See also Grelling's Paradox
References
Courant, R. and Robbins, H. ``The Paradoxes of the Infinite.'' §2.4.5 in What is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed. Oxford, England: Oxford University Press, p. 78, 1996. Frege, G. Foundations of Arithmetic. Evanston, IL: Northwestern University Press, 1968. Hofstadter, D. R. Gödel, Escher, Bach: An Eternal Golden Braid. New York: Vintage Books, pp. 20-21, 1989.
- Definite Integral
- Degenerate
- Degree
- Degree (Algebraic Surface)
- Degree (Map)
- Degree of Freedom
- Degree (Polynomial)
- Degree Sequence
- Degree (Vertex)
- Dehn Invariant
- Dehn's Lemma
- Dehn Surgery
- de Jonquières Theorem
- de Jonquières Transformation
- Del
- de la Loubere's Method
- Delannoy Number
- Delaunay Triangulation
- Delian Constant
- Delian Problem
- de Longchamps Point
- Del Pezzo Surface
- Delta Amplitude
- Delta Curve
- Delta Function