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Did You Find Out? Get the Answer to the Riddle of E-News Issue No. 01, February 2016

The witch recites a spell beginning with the puzzling verses of Goethe's witch`s one-times-one.
The witch recites a spell beginning with the puzzling verses of Goethe's witch`s one-times-one.

Two old witches brew a magical rejuvenation potion in their kitchen. Before they drink the mysterious cocktail, one of the witches recites a spell. It begins with the puzzling verses of the witch`s one-times-one of Goethe's famous "Faust".

"This you must ken!
From one make ten,
And two let be,
Make even three,
Then rich you'll be.
…”

With the witch's one-time-one, Johann Wolfgang von Goethe swirled the world of numbers properly. But who knows, maybe the famous poet was inspired by the equation below. This seems to prove that 2 = 1is that right?

                  a = b                       | • a            We multiply both sides by “a”

                 a² = a b                    | + a²           Now we add on both sides “a²”

         a² + a² = a b + a²               | - 2ab          Then we subtract ”2ab”

a² + a² - 2ab = a b + a² - 2ab                           … and calculate (simplify)

      2a² - 2ab = a² - ab                                   … and exclude

  2 • (a² - ab) = 1 • (a² - ab)          | : (a² - ab)   Finally, both sides are divided by “(a² - ab)”

                  2 = 1

Solution

The calculation begins with the equation a = b.

However, if a = b, then a² = ab and thus the expression (a ² - ab) is equal to zero. In the last step of the calculation it is therefore divided by zero, which is generally known to be prohibited in mathematics. Thus, the supposed proof that 2 = 1, is wrong and with the witch`s one-times-one Goethe cannot rely on mathematics but only to his poetic license.


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