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Fernando Revilla
science forum Guru Wannabe

Joined: 10 May 2005
Posts: 102

Posted: Thu Jul 13, 2006 11:56 am    Post subject: Re: Why you can not count real number?

 Quote: Is there any problem if I make a hypothesis that real number is countable? Just the probability that you can make more and more number as you go?

" Kant notably holds that arithmetic is synthetic a priori
and has to do with the pure intuition of time."

The fundamental idea is that in the process of counting
we freeze time, nothing to do with the continuum.

Independently of this, the concept of bijectivity solve your
question in negative sense.

Regards, Fernando.
kunzmilan@atlas.cz
science forum beginner

Joined: 21 Feb 2006
Posts: 42

 Posted: Thu Jul 13, 2006 9:59 am    Post subject: Re: Why you can not count real number? The list of all ratios 0/inf, 1/inf, 2/inf, till inf/inf couns all real numbers in the range 0-1, regardless of definition of infinity. Between them [square root from 2]/inf is not included, since [square root from 2] was not in the original list of the natural numbers. Similar arguments are true for any [square root from 2]/k, k =/> 2. kunzmilan
Virgil
science forum Guru

Joined: 24 Mar 2005
Posts: 5536

Posted: Tue Jul 11, 2006 1:53 am    Post subject: Re: Why you can not count real number?

albstorz@gmx.de wrote:

 Quote: and real numbers in geometry.

Speak for yourself, Al. There are lots of differences.
 Quote: The one who likes to state, that there is a necessarity of more real than natural numbers are very dogmatic people.

In ZFC or NBG, there are more reals in the sense that there are
injections but no surjections from N to R.
albstorz@gmx.de
science forum Guru Wannabe

Joined: 11 Sep 2005
Posts: 241

Posted: Mon Jul 10, 2006 9:34 pm    Post subject: Re: Why you can not count real number?

 Quote: Is there any problem if I make a hypothesis that real number is countable? Just the probability that you can make more and more number as you go?

There are concepts in which the real numbers are uncountable in the
sense of being a greater set than other infinite sets, e.g. the set of
natural numbers.

But there are also concepts in which you can't found differences
between the "amount" (or cardinality of the sets) of natural and real
numbers.
E.g, you can't found differences between the amount of natural numbers
and real numbers in geometry.

The one who likes to state, that there is a necessarity of more real
than natural numbers are very dogmatic people.

Best regards
Albrecht S. Storz
Phil Carmody
science forum Guru Wannabe

Joined: 05 Jun 2005
Posts: 267

Posted: Mon Jul 10, 2006 9:29 pm    Post subject: Re: Why you can not count real number?

"Randy Poe" <poespam-trap@yahoo.com> writes:
 Quote: phadamasci wrote: Mike Deeth wrote: This is no problem, it is well known that the reals can be paired up with the integers in a natural way, and this is what it actually means for a set to be countable. I'm surprised to hear that pairing up the reals with the integer in a natural way is possible. That's because Mike Deeth aka Nathan the Great who has ranged from 11 to 13 years old for at least a decade, is one of the sci.math cranks who thinks the reals are countable. It isn't "well known" because it isn't true.

Isn't he a troll, rather than a crank? I don't think he believes
the bollocks he posted any more than you or I do.

I bet he's tallying as we speak...

Phil
--
The man who is always worrying about whether or not his soul would be
damned generally has a soul that isn't worth a damn.
-- Oliver Wendell Holmes, Sr. (1809-1894), American physician and writer
Randy Poe
science forum Guru

Joined: 24 Mar 2005
Posts: 2485

Posted: Mon Jul 10, 2006 8:59 pm    Post subject: Re: Why you can not count real number?

 Quote: Mike Deeth wrote: This is no problem, it is well known that the reals can be paired up with the integers in a natural way, and this is what it actually means for a set to be countable. I'm surprised to hear that pairing up the reals with the integer in a natural way is possible.

That's because Mike Deeth aka Nathan the Great who has
ranged from 11 to 13 years old for at least a decade, is one of
the sci.math cranks who thinks the reals are countable.

It isn't "well known" because it isn't true.

 Quote: Would you recommend text or website that I can refer to? I don't care whether the thing is incomplete version..

I'd like to see if "young" Nathan the Great can provide one
of these rigorous analysis texts that supposedly contains this
bijection.

- Randy
Gene Ward Smith
science forum Guru

Joined: 08 Jul 2005
Posts: 409

Posted: Mon Jul 10, 2006 8:58 pm    Post subject: Re: Why you can not count real number?

 Quote: Mike Deeth wrote: This is no problem, it is well known that the reals can be paired up with the integers in a natural way, and this is what it actually means for a set to be countable. I'm surprised to hear that pairing up the reals with the integer in a natural way is possible.

Don't pay attention to the little man behind the curtain. He's just
trying to confuse you.
Rick Decker
science forum Guru Wannabe

Joined: 28 Apr 2005
Posts: 210

Posted: Mon Jul 10, 2006 8:57 pm    Post subject: Re: Why you can not count real number?

 Quote: Mike Deeth wrote: This is no problem, it is well known that the reals can be paired up with the integers in a natural way, and this is what it actually means for a set to be countable. I'm surprised to hear that pairing up the reals with the integer in a natural way is possible. Would you recommend text or website that I can refer to? I don't care whether the thing is incomplete version.. Thanks It is well known that the set of all real numbers CANNOT be "paired up"

with the integers. Deeth is a well-known troll--pay him no mind.

Regards,

Rick
cyclomethane@gmail.com
science forum beginner

Joined: 02 Jul 2006
Posts: 5

Posted: Mon Jul 10, 2006 8:53 pm    Post subject: Re: Why you can not count real number?

Mike Deeth wrote:

 Quote: This is no problem, it is well known that the reals can be paired up with the integers in a natural way, and this is what it actually means for a set to be countable.

I'm surprised to hear that pairing up the reals with the integer in a
natural way is possible. Would you recommend text or website that I can
refer to?
I don't care whether the thing is incomplete version..
Thanks
Mike Deeth
science forum beginner

Joined: 07 Jul 2006
Posts: 4

Posted: Mon Jul 10, 2006 6:45 pm    Post subject: Re: Why you can not count real number?

 Quote: Is there any problem if I make a hypothesis that real number is countable? Just the probability that you can make more and more number as you go?

This is no problem, it is well known that the reals can be paired up
with the integers in a natural way, and this is what it actually means
for a set to be countable. Some extremists will dispute this, they are
holdouts from a more primitive time and prove the old phrase, "science
progresses funeral by funeral". If you need a formal proof of the
counability of the reals, most rigorous analysis texts will provide
one.

Hope this helps =)
Nathan the Great
Age 11
BuddhaThu
science forum beginner

Joined: 06 Oct 2005
Posts: 21

Posted: Mon Jul 10, 2006 4:23 pm    Post subject: Re: Why you can not count real number?

Yes, real numbers can be counted. They are discrete and finite, even
though their purpose of existence is to measure continuity.

Any real number no matter how small will always be finite, i.e. .5,
..55, .555, .55555,.5555555 etc...

It will possess the Archimedean property.

The infinitesimal, however, expressed as 1/x is a whole new different
structure. It will supersede all positive and discrete real numbers
above.

It generalizes the direction of real into a vector of infinity. There
is no more counting, i.e. .555555555555555555555555555555 ad infinitum.

B.T.

 Quote: Is there any problem if I make a hypothesis that real number is countable? Just the probability that you can make more and more number as you go?
Dave Seaman
science forum Guru

Joined: 24 Mar 2005
Posts: 527

Posted: Mon Jul 10, 2006 12:54 pm    Post subject: Re: Why you can not count real number?

On 10 Jul 2006 04:59:41 -0700, phadamasci wrote:
 Quote: Is there any problem if I make a hypothesis that real number is countable?

Any single real number is countable. It's the set of all real numbers
that is uncountable.

 Quote: Just the probability that you can make more and more number as you go?

Some sets, such as the rationals, are countably infinite. To say that a
set is uncountable is much stronger than merely saying the set is
infinite.

--
Dave Seaman
U.S. Court of Appeals to review three issues
concerning case of Mumia Abu-Jamal.
<http://www.mumia2000.org/>
David C. Ullrich
science forum Guru

Joined: 28 Apr 2005
Posts: 2250

Posted: Mon Jul 10, 2006 12:16 pm    Post subject: Re: Why you can not count real number?

On 10 Jul 2006 04:59:41 -0700, "phadamasci" <cyclomethane@gmail.com>
wrote:

 Quote: Is there any problem if I make a hypothesis that real number is countable?

Yes, because the real numbers are _not_ countable.

 Quote: Just the probability that you can make more and more number as you go?

************************

David C. Ullrich
cyclomethane@gmail.com
science forum beginner

Joined: 02 Jul 2006
Posts: 5

 Posted: Mon Jul 10, 2006 11:59 am    Post subject: Why you can not count real number? Is there any problem if I make a hypothesis that real number is countable? Just the probability that you can make more and more number as you go?

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