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

236

CARDINAL ARITHMETIC

[PART III

*121-601. I-:E! B'P. ).B'P= lp.r(B'P) P,)(B'P)I
*121-602. F:E!B'P.Pcl-+l 1.D.P'B'P=2p
*121-634. F:.PECls ---1 IPp0CGJ.veNCinduct-t'0.:):
vp eD'P. =E. E! (v~+,,l)p
Finally we have three propositions (*121-7 —72) on 1?*'x, of wvhich the
most useful is
*121-7. F: R e1 — 1. aBR.aR*x.)D. B*'x=R(a t~-qx).BR*'xeClsinduct
*121-01. P (x- y) P 'x A P1Cy Df
*121-012. P (x-y) = P*jx mP,'y Df
*121-012. P (x- y) = P*'x ri P*0y Df
*121013. fndP(c y)= P*'wgvP.vyNCiduttA =PI D
*121-031. fin'P = R {(av). v E NC induct - tA- t'0. R = P~} Df
*121-04. vp = Pv-cl'B'P Df
*121-1. F: zE6P (c- y).u.xPP0z. ZPPy [(*121-01)]
*121-101. F:z eP (x -— y). xcPP0z. zP*y
*1214102. F:z eP (x ~ —y). xcP*z. zP,0y
*121-103. F:z isP (xny). xP~z. zP~y
*121-11. F:xP y. = N,,c'P (xc ~-y) = ~+,I1 [(*1 2102)]
*121-12. F B RE finid'P..(afv). v e NC induct - tA. R = P, [(*1 21-03)]
*121-121. F B e fi n'P..(d[v). v e NC I nd uct - 'A -t'0. R = P [(*121-031)]
*121-13. F: f(vp)..f(Pv-c1'B'P) [(*I121-04)]
*1214131. F: E' P__/'P.) jP(1B'P [*121-13. *1 428]
*121-14. F. P (x- y) = P (y -c) [*121-1. *91-53]
*1214141. F.-P (x — iy) = P(yFX)
*1214143. F.-P(xc~-y)=P(y~ —~c)
*121-201. F:c-<yPpoy) D.yr.e P (x -y)