"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?
Reminds me of this: I has a mathematical system!
ReplyDeleteWell, 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.
ReplyDeleteUseful? Yes. And in the same spirit.
ReplyDeleteEarly 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
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.
ReplyDelete