[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.

[Billthedrill]

Very good! I never made it to volume two of the Principia - made my poor head hurt. But to Russell (and, I think, Whitehead still at that point) it would have been "S0 + S0 = SS0" - the trick was mapping "SS0" to our numeral "2." I'm still not sure how Russell did that, but Godel had it figured out.