Sunday, April 10, 2016

The Perfection of Penguins: an inductive proof

In mathematical induction, you begin with the base case a.k.a. Induktionsanfang, traditionally symbolized as P(0) (where P stands for “Penguin”, and  0 depicts the egg).   In the present instance, P(0) is Baby Fuzzy.

Kleiner Kuschel-Induktionsanfang
Now, P(1) = Fuzzy’s Mommy;  and they rejoice in a Perfect Love.  Thus, the Induction Hypothesis is established.
Now consider any arbitrary P(k).  In this case, P(k)  is known as Fluffy;  and P(k +1) (the k-plus-first Penguin) is Fluffy’s perfectly adoring mate.   So once again, the induction goes through.
Thus we have established the Perfection of Penguins.
Note:  Using the more powerful technique of Transfinite Induction, we can establish the existence of (the wonderful, the unutterable) Zorn’s Penguin.   This, however, requires the Axiom of Choice, in its strengthened form, “Choose Penguinity”.

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