Re: Logarithm of transfinite numbers


stephen@xxxxxxxxxx wrote:
matt271829-news@xxxxxxxxxxx wrote:
stephen@xxxxxxxxxx wrote:
That is what Cantor did all those years ago.

Didn't he go bonkers or something? I can't say I'm surprised!

Probably because he had a vision of Usenet and the endless
threads arguing about what is in essence a very simple idea.

Stephen

People thought Goedel's results about incompleteness in logical
theories were sublime as well, yet in modern thought about it there are
a variety of ways to consider that they don't hold.

In some cases, they involve Cantor's diagonal argument not holding
true.

You think those are simple ideas? Infinity is for you cut and dried
and completely described? No, it's not, because if you believe Cantor
then you believe Goedel, and thus you can never be sure of _anything_.

The universe is infinite. Infinite sets are equivalent.

If not, then there is no universe. So, in an empirical manner, the
mere fact of existence is also that infinite sets are equivalent.

It's pretty obvious that among all points of discussion, at least here,
about mathematics, the contention is almost solely about infinity, and
to some extent that the "Cantorians", or adherents of basically...,
well it's not quite simple to describe, of basically the powerset and
nested intervals results but a denial of any other notions as having
meaning, that there is a prejudice against what to many classical and
modernly superstandard mathematicians is obvious, intuitive, and
according to some, e.g. me, rigorously provable.

Consider for example the convergent sum of an infinite series. No, not
a a limit, the whole thing. That has infinitesimals in the reals, and
infinite values in the integers, for example.

Indeed, one notion that has resulted as an extension of the study and
interpolation of Goedel's results is that there are infinite values, or
an infinite value, in the natural integers, and a variety of basically
modern and well-informed notions use that to even circumvent
incompleteness anyways.

If you actually care about the infinities and infinitesimals in your
theory, in terms of the numbers there, then you'd be remiss to not
investigate pretty obvious (to some) justified reasonings about them,
as for example have been presented here.

People argue about infinities becausee they disagree. There isn't
anything else on this newsgroup that remotely compares. There isn't
large amounts of contentious discussion about any other subject, in
mathematics.

If Cantor was promoting his concepts in the days of usenet and the
Internet, how do you think he would?

THE universe is infinite.

Ross

.

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