Fallacy
A fallacy is an incorrect result arrived at by apparently correct, though actually specious reasoning. The most common example ofa mathematical fallacy is the ``proof'' that 
as follows. Let 
, then
The incorrect step is division by
(equal to 0), which is invalid. Ball and Coxeter (1987) give other such examples inthe areas of both arithmetic and geometry.
References
Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, pp. 41-45 and 76-84, 1987. Pappas, T. ``Geometric Fallacy & the Fibonacci Sequence.'' The Joy of Mathematics. San Carlos, CA: Wide World Publ./Tetra, p. 191, 1989.
- Carmichael Number
- Carmichael's Conjecture
- Carmichael Sequence
- Carmichael's Theorem
- Carmichael's Totient Function Conjecture
- Carnot's Polygon Theorem
- Carnot's Theorem
- Carotid-Kundalini Fractal
- Carotid-Kundalini Function
- Carry
- Carrying Capacity
- Cartan Matrix
- Cartan Relation
- Cartan Subgroup
- Cartan Torsion Coefficient
- Cartesian Coordinates
- Cartesian Ovals
- Cartesian Product
- Cartesian Trident
- Cartography
- Cascade
- Casey's Theorem
- Casimir Operator
- Cassini Ellipses
- Cassini Ovals