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

86

CARDINAL ARITHMETIC

[PART III

*10-632. F:,ue NC /z [(g, =i(y) - y e t.F 'y e sm",41
Dern.
F. *110-631. *51211-22. )
F: Hp.., +~, 1 = 4 {(aH'Y Y). y c sm"tk. y E 4: 4 - t/y}
[*13-195] = Ra(~y). Y E 4:- ffYE smccj: II F. Prop
*110-64. F. 0 +c 0 = 0 [*I110'62]
*110-641. F. Io=o+,l ~1 1 [*110-5161. *101-2]
*110-642. F. 2-I0=0~+, 2=2 [*110.51-61.*101P31]
*110-643. F. 1+ I=2
Dem.
F. *110632. *101-2128. D
F. 1 +C 1 = 4:(ajy. y e. 4:- ify ell
[*54-3] = 2.DF.Prop
The above proposition is occasionally useful. It is used at least three
times, in *113-66 and *120-123-472.
*110-7-71 are required for proving *110-72, and *110-72 is used in
*117-3, which is a fundamental proposition in the theory of greater and less.
*c110-7. F-: 8 C at.~.(C).~ e NC. Ne'aa = Ncl,8 +c t
Demn.
F. *24-41121. F: Hp. a=. u (a-/3).flA (a -/) = A.
[*110-32] D.Nc'a = Nc', +, NC(a - P): D F. Prop
*11071. F:(L).Nc'a=Nc' +, t.)..3snhI3..3Ca
Dem.
F. *100-3. *110-4.
F: Nc'a = Nc'/3 +,a. ). -t e NC - (1)
F. *110-3. ) F: Nc'a = Nc',3 +, Ncry.. Nc'a = Nc'(fl + #y).
[*100-3-31 D. asm (& +ry).
[*73-1]. (aR). Re 1 -*1. D'R = a (I'R= A,"t"/3vn 4, "t"ey.
[*37 15]:. (RR). R e 1. Ay CtLc,8 C W'R R" I Xyl Y"8~ C ar.
[*110-12.*73-22] ). (Hjc3). c Ca. 8 sm. (2)
F.(1).(2). DF. Prop