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Pythagoras drogredeneringen: De oplossingen<br>door Andé de Boer

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Pythagoras drogredeneringen

De oplossingen
door Andé de Boer

Oplossing "Elk getal is groter dan zichzelf"

Eerst een voorbeeld. We beginnen met de positieve getallen a=3 en b=2. Vermenigvuldig beide getallen met b=2. Dan krijgen we

$\begin{displaymath}3\cdot2>2^2. \end{displaymath}$

Trek nu links en rechts 3² af:

$\begin{displaymath}3\cdot2-3^2>2^2-3^2. \end{displaymath}$

Ontbind in factoren:

3(2-3)>(2-3)(2+3).

Tot nu toe klopt alles, want er staat -3>-5. Nu delen we beide leden door 2-3=-1. Er staat dan niet 3>5, maar:

3<5.

Immers, bij deling door een negatief getal klapt het ongelijkteken om. Hierin zit dus de fout: we delen door b-a, en dat getal is negatief omdat we aannamen dat a>b.

Verder naar de redenering 1=2 (II).
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Laatst bijgewerkt op:
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Friday 6 June 2003, 14:00

Pythagoras drogredeneringen

De oplossingendoor Andé de Boer

Oplossing "Elk getal is groter dan zichzelf"

De oplossingen
door Andé de Boer