Principia mathematica, by Alfred North Whitehead ... and Bertrand Russell.

SECTION D] THE SUMT OF TWO RELATION-NUMBERS 481
*180-551. F.(Nor'P -I-N~r'Q) -I-Nr'R =Nor'P4- (Nor'Q -I-Nr'R)
*180571. Ff
*18065. F:,LLNR.).0rsnor"V t0<
Observe that tk -- 0,. = 0,. -1- IL is an equation depending upon the peculiar
properties of Or* We do not ini general have /. 4- v =v -I- t unless u andi v are
finite ordinals.
*180-61. F.Nr'14O,-1-= Nr'1 = Or - Nr'I-)
*180-62. F/t1vO.~rLO.vO
*180-64. F Or 4- 0r Or
*180-642. F. 2rt+Or01,=0rt2r =2,.
Note that 1 O-1-0., which wviii be definted in *1 81, is 0,., not 1
The following propositions, being concerned with the relations of relationnumbers and cardinal nunibers, have no analogues in *110.
*180-7. F.C"Nr'(P- + Q) = C"Nr'P ~C C"'Nr'Q = Nc'C'P +,, Nc'C'Q
Dern.
F. *152-7.)F. C"Nr'(P ~ 9) Nc'C'(P + Q)
[*180-111] -Nc'(C'11 + C'Q)
[*110-3] -Nc'C'1- +0, NcC'CQ (1)
[*152-7] C"Nr'1- +0, C"Nr'cQ (2)
F.(1). (2). ) F. Prop)
*180-71. F:,a,PeNR.~ ). J(,-i-V) = G" 6+c C6
Dent.
F. *152-4. ) F:Hp.).(a[P, Q).p= Nr'P. v= Nr'Q9.
[*180-7] )(gjP, Q). = Nr'P. P= Nr'Q.
6 (u-1- v) C= 'JNr'P ~0 J"Nr' Q.
[*13-193] ). %U" - V) =6 C", +0 G66v: ) F. Prop
R. &W. II..3