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6.02

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

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

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

"[⁰, ^v'x, ^v+1'x]",

And I define:

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

6.021

A number is the exponent of an operation.

6.022

The concept number is nothing else than that which is common to all numbers, the general form of a number.