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Paradokslar
=> Zeno's Paradoxes
=> Allais Paradox
=> Arnauld's Paradox
=> Banach-Tarski Paradox
=> Barber Paradox
=> Berry Paradox
=> Bottle Imp Paradox
=> Buchowski Paradox
=> Cantor's Paradox
=> Catalogue Paradox
=> Coin Paradox
=> Complex Number Paradox
=> Crocodile's Dilemma
=> Destructive Dilemma
=> Diagonal Paradox
=> Dilemma
=> Elevator Paradox
=> Epimenides Paradox
=> Eubulides Paradox
=> Grelling's Paradox
=> Hempel's Paradox
=> Liar's Paradox
=> Line Point Picking
=> Missing Dollar Paradox
=> Newcomb's Paradox
=> Parrondo's Paradox
=> Potato Paradox
=> Richard's Paradox
=> Russell's Antinomy
=> Skolem Paradox
=> Smarandache Paradox
=> Socrates' Paradox
=> Sorites Paradox
=> Strange Loop
=> Thompson Lamp Paradox
=> Unexpected Hanging Paradox
=> Fallacy
=> Plaindrome
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Fallacy

fallacy is an incorrect result arrived at by apparently correct, though actually specious reasoning. The great Greek geometer Euclid wrote an entire book on geometric fallacies which, unfortunately, has not survived (Gardner 1984, p. ix).

The most common example of a mathematical fallacy is the "proof" that 1=2 as follows. Let a=b, then

ab=a^2
(1)
ab-b^2=a^2-b^2
(2)
b(a-b)=(a+b)(a-b)
(3)
b=a+b
(4)
b=2b
(5)
1=2.
(6)

The incorrect step is (4), in which division by zero (a-b=0) is performed, which is not an allowed algebraic operation. Similarly flawed reasoning can be used to show that 0=1, or any number equals any other number.

Ball and Coxeter (1987) give other such examples in the areas of both arithmetic and geometry.

 

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