[Aurelius]

"Though it took Bertrand Russell, in his Principia, some 400 pages to rigorously prove that 1+1=2."

I may be wrong, but I would doubt that "1 + 1 = 2" is a proposition in Principia Mathematica.

[onedoug]

I thought it was, in Russell's.

I also thought to goof on Fermat's "Last" Theorem, but can't manage the HTML. Oh, well....

[jejones]

Trust me, it is; the proposition and its proof are in Volume 2. (The "400 pages" is all the preceding material, not just the proof of 1 + 1 = 2.) I don't have a copy of all of PM (I wish I did, but it's $800 or so!), but I do have the paperback with the first 56 chapters, and near the end is a proposition, "if a and b are elements of 1 and disjoint, then a union b is an element of 2" (remember, R&W use the Frege definition of the cardinal numbers, in which n is the set of all sets with n elements, though of course the definition is framed to avoid circularity!). R&W comment that this proposition will be used later to prove that 1 + 1 = 2.