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

380

380 ~~PROLEGOMENA TO CARDINAL ARITHMETIC [ATI

[PART 11

[*54-441]
*54-443. F:: x +y: (x, y).Bfyx):.
Zw,WEt'Xut'Y.Z4w.:)z,w-cf(z,w):-.O(x,y) [*54-442]
*54-451. F::.,O(x,x).cc(y,,y). ):.(afz,w).z,wet',xv t'y.o(z,w).
(rHZ, w).-Z, w 6trx v Lcy -(z, W)..q(x, y) [*54-4511

*54-46. F:(a~z,w).z,wEt'xvt'yl.z~w.-=.x+y [*5"4-452.*1315-1
*54-5. F:.a E2.) a Ctfzv t'w.=* a =t vt
Dem.
F. *54 4.)
F:. aC t'z v tw.:):a= A.v * a=l. v *a =tii w *v *a = vz
F. *54-3.-*24-54.:) F: Hp.- ). a + A
F. *54-26 Z'Z. *13-15. D F: Hp. D. a+t'z
F. (1). (2). (3). (4). *205:3. D F:. Hp. ): a C t'z u '.'w. a= tfz v ~
F. *22-42. D F: a= t'z v t'w. D. a C i'z v ~
F.(5).(6). DF. Prop
*54-51.F:a2/E2.:C3.=3
Dern.
F.(1).*1113545. D
F:. a E 2: (Hz, w)., /3 -~ v t'w:): a C /3 * = /3
F.(2). *54-271..)F. Prop
*54-52. F:a/e.:C3~a/..3a [*54-51]
*54-53. F:aE62.x,yca.x+,y.:).a=tfxvt'y
Dern.. *51-2.:)F:Hp.:).t'xCa.t'yCa.
[*22-59]:). fx v t'yC a
F. *54-26. F::Hp.:). tfxvffty e2
F.(1).(2). *54-52. F. Prop

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