Page:Cantortransfinite.djvu/125

From Wikisource
Jump to navigation Jump to search
This page has been proofread, but needs to be validated.
106
THE FOUNDING OF THE THEORY

Hence follows that , and therefore .

From A and B the formula (4) results, if we have regard to §2.

From (2) we conclude, by adding to both sides,

,

and, by repeating this

(5)
.

We have also

(6)
.

[494] For, by (1) of §3, is the cardinal number because

.

Now, obviously

,

,

and therefore

.

The equation (6) can also be written

;

and, by adding repeatedly to both sides, we find that

(7)
.

We also have

(8)
.