Re: ** says: Definition: sum{i in N} i = 0

In article <1184001296.370640.104990@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
WM <mueckenh@xxxxxxxxxxxxxxxxx> wrote:

On 9 Jul., 19:00, hagman <goo...@xxxxxxxxxxxxx> wrote:

2) that Liouville did not create uncountably many transcendental
numbers.

IIRC, he showed that any number that can be approximated
unusually well is transcendental and gave sum 10^(-n!)
as a simple example of an unusually well approximable number.

Yes, you remember correctly.

He would hardly have been surprised to hear that all the
numbers sum a_n*10^(-n!) are transcendental.

Perhaps he would not even have doubted to be able to use all the
infinite sequences you defined. Nevertheless he would have been as
unable to do so as is everybody else. Therefore he did not create
uncountably many transcendental numbers.

AS they were all there before he came on the scene, he did not create
any of them, but he did identify them as irrational and even
transcendental.

And WM is still conflating the mathematical existence of a number with
its having been physically written down in some positional notation.

Writing down numbers is a problem in physics, not mathematics.
.