Re: Gary Forbes - are you still around? I want to ask you about the cardinalities of infinity.

[Antti J Ylikoski]

On 7.5.2015 7:07, Don Stockbauer wrote:
> A few years back I claimed that the infinity of integers is as "strong" as the infinity of reals, and you began a proof that that is not the case, and I did not let you go on, and basically I want to see what you would have had to say.
> Thanks.
>

The cardinality of the set of integers is denumerable, i. e. aleph zero.

The cardinality of the set of reals is uncountable, i. e. greater than
aleph zero. (See the continuum hypothesis.)

yours, DLitt Antti Ylikoski
HELSINKI
Finland
The E.U.

http://koti.mbnet.fi/bluejay/

[el gato loco]

On Wednesday, May 6, 2015 at 10:07:14 PM UTC-6, Don Stockbauer wrote:
> A few years back I claimed that the infinity of integers is as "strong" as the infinity of reals, and you began a proof that that is not the case, and I did not let you go on, and basically I want to see what you would have had to say.
> Thanks.

This is easy to prove. The integers cover a length of zero since they are M zero length pieces, where M can be any large number chosen. The real numbers on the other hand, cover infinite length, since choose any M as large as you want and you can lay down reals large enough to cover that length.
--
My math talk is rusty.

[el gato loco]

On Thursday, May 7, 2015 at 9:21:30 PM UTC-6, Don Stockbauer wrote:

> You can't prove math assertions by using the physical world.
>
> What I was thinking of in the my first post was that when you do Cantor
> diagonalization you can index each produced diagonal number with an integer, and you never run out of integers. However, I don't believe that gets you anywhere on second thought.

It sounds like you are working on the nextmost difficult proof, that the Rationals are not as "strong" (dense is a nice word) as the reals which are the rationals plus the irrationals.
--
I just realized Cantor has two claims with his name and there are few with such. René Descartes comes to mind.

[el gato loco]

On Friday, May 8, 2015 at 4:22:20 PM UTC-6, Don Stockbauer wrote:

> Rene had a sleepless night.

Call me Emmanuel.

[el gato loco]

On Friday, May 8, 2015 at 8:42:58 PM UTC-6, Don Stockbauer wrote:

> Call me Ishmael.
>
> Call me a taxi.

You know that I would do anything to give you a kiss in the back of a taxi.

[el gato loco]

On Sunday, May 10, 2015 at 2:21:17 PM UTC-6, Don Stockbauer wrote:

> I would resist that.

At the same time I would be
pulling feints with my hand
towards your underwear. You
would keep raising your eyes,
yet never be able to swat away
my hand because I know it is
crude to put a hand on a woman's
zipper before she takes off her
clothes for the first time. So
I would never touch you. What do
you do now?
--
What are you doing in the back
of the taxi with me anyway? I might
get my peanut butter in your
chocolate.

[el gato loco]

On Sunday, May 10, 2015 at 9:20:55 PM UTC-6, Don Stockbauer wrote:

> The wonders of the Internet. There's no way I can convince you that I am
> male. So dream on.

I'm convinced that you have a hell of a control system to slide in so well and almost blend. Either that or you are in your male internet persona butch and fuckall like you think a man is supposed to be. And you have pink socks and a green shirt on and a bowtie that is attractive even if your whiskers are there.

[Antti J Ylikoski]

On 05/09/2015 01:22 AM, Don Stockbauer wrote:

> Rene had a sleepless night.
>

Albert Einstein has several.

AJY
Helsinki, Finland

[Antti J Ylikoski]

On 05/18/2015 02:58 AM, Don Stockbauer wrote:
> Yes, I'm sure Einstein did. But no longer.
>

Sorry, D.B., I communicated badly. English is not my mother tongue!

I intended to say that Einstein had a number of immortal statements
credited to him. Special relativity; general relativity; the
photoelectric effect; and some additional ones.

I have read two biographies of Einstein, and I assume that Albert E. did
not have many, if any, sleepless nights. Well, E. was one of the
creators of the nuclear bomb, but I understand that this fact never was
considered in any manner ethically bad or evil by him.

Dr Antti Ylikoski
Helsinki, Finland

[Jeff Barnett]

You have read quite different biographies then I have. I believe he was
quite concerned and spoke out.
--
Jeff Barnett

[Antti J Ylikoski]

Hi Jeff:

Concerned yes; but not someone who would think he had been EVIL. Two
different points!

Be precise about statements!

--AJY

[Antti J Ylikoski]

On 05/19/2015 06:02 AM, Don Stockbauer wrote:

> DesCartes' sleepless night was not from him worrying that he had done evil deeds. It was a night of profound mental agitation, and during it he came to such conclusions as "I think, therefor I am". Einstein was caught up in defeating the Axis powers at all cost, and along with his fellow physicists he did not foresee the magnitude of long term evil, arming the planet to the hilt with nuclear weapons.
>


Have you seen Arthur C. Clarke's CHILDHOOD'S END as a movie?

In the movie, an ape discovers that it is possible to grab a bone, and
hit an object with it.

The ape finds out that he can break dry bones with that bone in his
hand; and quite obviously he can hit other apes, and hit menacing tigers
with the bone in his hand.

(Glorious music in the background.)

That was, in the movie, the point in time, when a TOOL was invented.

And the Black Monolith watches in the background.

Science, knowledge, wisdom, is like that. It gives the human being a
great power for good, and a great power for evil.

Scenarios such as the MAD, the Mutual Assured Destruction, are indeed
evil. But the question about the moral-ethical status of nuclear
technology is an extremely nontrivial political question -- to my modest
opinion.

Cheers, A. J. Y.
Helsinki, Finland

http://koti.mbnet.fi/bluejay/