Re: Logarithm of transfinite numbers

In article <MPG.1e835c7f21657d6098ab00@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow <aeo6@xxxxxxxxxxx> wrote:

stephen@xxxxxxxxxx said:

More precisely,
there are lots of arrangements of aleph_0 bits that do
not correspond to a natural number. There is no "number infinity"
in the natural numbers. Every natural number can be represented
by an arrangment of aleph_0 bits that contains only a finite number
of 1's. Not every arrangement of aleph_0 bits only contains
a finite number of 1's.

That is entirely incorrect.

TO is entirely incorrect in saying that.

With which part (or parts) precisely does TO disagree?

(1) there are lots of arrangements of aleph_0 bits that do
not correspond to a natural number

or
(2) There is no "number infinity" in the natural numbers.

or
(3) Every natural number can be represented
by an arrangment of aleph_0 bits that contains only a finite

number 1's
or
(4) Not every arrangement of aleph_0 bits only contains
a finite number of 1's.

Since all of these parts are trivially provable in standard mathematics
assuming any of several representation schemes, TO must be wandering
around lost in his TOmatic wonderland again.
.