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The “No WAY!” The “No WAY!” moment in moment in

mathematicsmathematics

A Countable SetA Countable Set

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A Countable SetA Countable Set

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A Countable SetA Countable Set

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A Countable SetA Countable Set

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A Countable SetA Countable Set

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A Countable SetA Countable Set

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A Countable SetA Countable Set

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The Diagonalization The Diagonalization ArgumentArgument

Georg Cantor

1876

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The Diagonalization The Diagonalization ArgumentArgument

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Cantor’s Original ArgumentCantor’s Original Argument

Georg Cantor

1874

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Cantor’s Original ArgumentCantor’s Original Argument

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Cantor’s Original ArgumentCantor’s Original Argument

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Cantor’s Original ArgumentCantor’s Original Argument

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Cantor’s Original ArgumentCantor’s Original Argument

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Cantor’s Original ArgumentCantor’s Original Argument

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Cantor’s Original ArgumentCantor’s Original Argument

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Cantor’s Original ArgumentCantor’s Original Argument

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Cantor’s Original ArgumentCantor’s Original Argument

L

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A Small Twist on Cantor’s Original A Small Twist on Cantor’s Original ArgumentArgument

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A Small Twist on Cantor’s Original A Small Twist on Cantor’s Original ArgumentArgument

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A Small Twist on Cantor’s Original A Small Twist on Cantor’s Original ArgumentArgument

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A Small Twist on Cantor’s Original A Small Twist on Cantor’s Original ArgumentArgument

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A Small Twist on Cantor’s Original A Small Twist on Cantor’s Original ArgumentArgument

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A Small Twist on Cantor’s Original A Small Twist on Cantor’s Original ArgumentArgument

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A Small Twist on Cantor’s Original A Small Twist on Cantor’s Original ArgumentArgument

...

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A Small Twist on Cantor’s Original A Small Twist on Cantor’s Original ArgumentArgument

... ...

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A Small Twist on Cantor’s Original A Small Twist on Cantor’s Original ArgumentArgument

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A Small Twist on Cantor’s Original A Small Twist on Cantor’s Original ArgumentArgument

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L

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L

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L

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L

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L

Therefore theGolden Ratiois irrational.