
Puzzles and Paradoxes in Mathematical Induction [pdf] - carlosgg
http://www.math.cornell.edu/~mec/2008-2009/ABjorndahl/ppmi.pdf
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deciplex
I was first exposed to mathematical induction in, I think, first-year algebra.
Although I was able to struggle through the work, I didn't really recognize
its power, and thought the whole thing a bit pointless. Blame either my young
brain or mathematics education.

A couple years later when I started to take programming more seriously and was
exposed to recursion, I did recognize the power there pretty quickly and made
a point of getting good at thinking that way. But, I didn't see the link then,
between mathematical induction and recursive functions. A few years after
_that_ , when I was exposed to mathematical induction again, it seemed like
such an obvious and powerful tool, and I was amazed that I didn't recognize it
for what it was on the first go around.

There is a saying:

 _when programming recursively, think inductively_

...but the inverse is also true:

 _when reasoning inductively, think recursively_

If you, or a student of yours, or your kid, or whatever, are having trouble
with either concept, I would encourage you to study the other one. You
probably can't truly understand one without groking the other anyway, and
insights gained from the study of one will apply pretty much directly to the
other.

This was an enjoyable read. Thanks.

