Ana Sayfa
Matematikçiler
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Matematik Seçkileri
Fraktallar
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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Ziyaretçi defteri
 

Complex Number Paradox

An improper use of the symbol sqrt(-1) for the imaginary unit leads to the apparent proof of a false statement.

sqrt(-1) = sqrt(-1)
(1)
sqrt((-1)/1) = sqrt(1/(-1))
(2)
(sqrt(-1))/(sqrt(1)) = (sqrt(1))/(sqrt(-1))
(3)
sqrt(-1)·sqrt(-1) = sqrt(1)·sqrt(1)
(4)
-1 = 1.
(5)

The reason for the fallacy is that sqrt(-1) is not an ordinary (real) square root, hence the rule for computing the quotient of radicals does not apply to it.

 

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