6.02 And thus we come to numbers: I define
x = Ω 0 ′ x Def. {\displaystyle x=\Omega ^{0\prime }x{\text{ Def.}}} and Ω ′ Ω ν ′ x = Ω ν + 1 ′ x Def. {\displaystyle \Omega ^{\prime }\Omega ^{\nu \prime }x=\Omega ^{\nu +1\prime }x{\text{ Def.}}}
According, then, to these symbolic rules we write the series x , Ω ′ x , Ω ′ Ω ′ x , Ω ′ Ω ′ Ω ′ x , . . . . . {\displaystyle x,\Omega 'x,\Omega '\Omega 'x,\Omega '\Omega '\Omega 'x,.....}
as: Ω 0 ′ x , Ω 0 + 1 ′ x , Ω 0 + 1 + 1 ′ x , Ω 0 + 1 + 1 + 1 ′ x , . . . . . {\displaystyle \Omega ^{0\prime }x,\Omega ^{0+1\prime }x,\Omega ^{0+1+1\prime }x,\Omega ^{0+1+1+1\prime }x,.....}
Therefore I write in place of “ [ x , ξ , Ω ′ ξ ] {\displaystyle [x,\xi ,\Omega '\xi ]} ”,
“ [ Ω 0 ′ x , Ω ν ′ x , Ω ν + 1 ′ x ] {\displaystyle [\Omega ^{0\prime }x,\Omega ^{\nu \prime }x,\Omega ^{\nu +1\prime }x]} ”.
And I define:
0 + 1 = 1 Def. {\displaystyle 0+1=1{\text{ Def.}}}
0 + 1 + 1 = 2 Def. {\displaystyle 0+1+1=2{\text{ Def.}}}
0 + 1 + 1 + 1 = 3 Def. {\displaystyle 0+1+1+1=3{\text{ Def.}}}
(and so on.)
and
![{\displaystyle [x,\xi ,\Omega '\xi ]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/647cd7f45d7d8e877cdb29758e7c4dd75f1d5dd5)
”,
![{\displaystyle [\Omega ^{0\prime }x,\Omega ^{\nu \prime }x,\Omega ^{\nu +1\prime }x]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2331b535de38ab1c66bb7d9acc00e76de6a08577)
”.
