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6.0

6.00
6.01
The general form of the operation  OMEGA ' ( eta-bar ) is therefore:
[ xi-bar , N ( xi-bar )]'( eta-bar ) (= [ eta-bar ,  xi-bar , N( eta-bar )]).

This is the most general form of transition from one proposition to another.

6.02
And thus we come to numbers: I define
x =  OMEGA 0'x Def. and
 OMEGA ' OMEGA v'x =  OMEGA v+1'x Def.

According, then, to these symbolic rules we write the series x,  OMEGA 'x,  OMEGA ' OMEGA 'x,  OMEGA ' OMEGA ' OMEGA 'x . . . . . as:  OMEGA 0'x,  OMEGA 0+1'x,  OMEGA 0+1+1'x,  OMEGA 0+1+1+1'x . . . . .

Therefore I write in place of "[x,  xi ,  OMEGA '  xi ]",

"[ OMEGA 0,  OMEGA v'x,  OMEGA v+1'x]",

And I define:


0 + 1 = 1 Def.
0 + 1 + 1 = 2 Def.
0 + 1 + 1 + 1 = 3 Def.
and so on.

6.03
The general form of the cardinal number is: [0,  xi ,  xi +1].


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