h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Thought you might like this one. Add it to your collection (if you don't have it already).

let a = b = 1
so:
.........a = b
.......a^2 = ab
...a^2-b^2 = ab-b^2
(a-b)(a+b) = b(a-b)
.......a+b = b
.......1+1 = 1
.........2 = 1

Isn't it lovely!

Of course, if we want a collection, we can generate as many apparent paradoxes based on division by zero (the zero in this case being (a-b), since a=b, if anyone hasn't noticed) as we like.

Well I did say it was impure!

Division by zero is a wonderfully disgraceful technique with which to molest so-called 'pure' mathematics.

Try searching for the 'Banach-Tarski paradox,' it'll blow your mind. Easier to understand is Russell's paradox, which gave mathematicians such a headache that they changed set theory to accommodate it. And, according to Roger Penrose (of the famous 'Penrose tilings'), the new version of set theory is both inprecise and contrived.

Don't you love mathematicians?

- Jordan