11 April 2008

Two quotes from Principia Mathematica (Russell and Whitehead)

"From this proposition it will follow, when arithmetical addition has been defined, that 1+1=2." -- a comment to proposition 54.43.
"The above proposition is occasionally useful." -- a comment to proposition 110.643, which proves that 1+1=2.

Quite the understatement, don't you think?

4 comments:

intrinsicallyknotted said...

Reminds me of this: I has a mathematical system!

Veky said...

Well, not really, I'd think. How useful 1+1=2 really is? It is in elementary mathematics, but not much in general abstract math - at least not without much more algebra.

jd2718 said...

Useful? Yes. And in the same spirit.

Early on in my Algebra I course we review (it's not always review) some properties of real numbers. I like talking about closure. The kiddies usually have not heard about closure. And we talk about "proof by counterexample". I present them with evidence that the natural numbers are not closed for subtraction.

And then I ask them to 'prove' something: "Show evidence that the set {0,1} is not closed under addition"

I should thank Bertrand Rusell every time I get to that spot...

Jonathan

Almost Philosopher said...

It's very useful in everyday life. So for all those people who carry Russell and Whitehead around at the supermarket it's certainly critical.