

The Hallmarks of Crackpottery, Part 1: Two Comments - timwiseman
http://scienceblogs.com/goodmath/2009/10/the_hallmarks_of_crackpottery.php

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BearOfNH
When I first saw the rationals placed in 1-1 correspondence with the integers
I pointed out there were lots of mappings that don't work, e.g., mapping every
integer to itself, thereby not having any integers left over for nontrivial
fractions. The instructor didn't have the right answer handy, and many of us
were confused. Sometimes Z and Q had the same cardinality, sometimes they
didn't?

Here's one answer: it's like saying you can get from New York to Boston, then
producing a map that demonstrates the route. There are many other routes that
don't take you to Boston, but so what? All you need do is demonstrate _A_ map
that gets you there -- you don't care about all the wrong ways to do
something.

I wish the instructor had hit me over the head with that at the time. Perhaps
we were too busy dodging Velociraptors and chasing those cute Neanderthal
girls...

