EFF claim(s)

[jinydu]

Originally Posted by bearnol

Well done jinydu!
I do just this (also) on my pages...
J

You misunderstood me there. I was saying that your "proof" is flawed because infinity is not an integer, and there certainly aren't infinitely many integers larger than infinity.

You would have to show that for infinitely many Mersenne numbers, Mp, there are no factors larger than the square root of Mp.

While it is true that the smallest possible factor grows as Mp grows, the square root of Mp also grows (in fact, it grows much faster).

Please understand that the "infinitely many Mersene primes" conjecture has stood unproven for centuries, and the chances of such a simple resolution, with no new major insights, are effectively zero.

[Peter Nelson]

I have been trying to locate the ACTUAL global dog population so that I can know how large this number is AND *SHOW* that it is prime for you skeptics.

Now I'm curious I actually want to know if my "billion dogs" was approximately right. So I set about some serious research. Thanks to Google and Ask Jeeves I turned up ....

"Speaking of statistics, The World Health Organization has done extensive studies on the global dog population, and yet no one seems to really know even approximately how many dogs roam the planet freely, which is a concern to me"
from
http://doctorhormone.com/blog/2005/0...ious-blog.html

That's not encouraging, I think we ought to KNOW these things.

Despite this, we do apparently know that.....

"with an estimated 15% of the global dog population affected by skin conditions due to allergy (Muller & Kirk's Small Animal Dermatology, 6th Ed, 2000). With around 90,000 affected animals in the UK, the canine dermatology market is estimated to be potentially worth GBP 10 million in the UK and GBP 100 million worldwide."

But that still doesn't tell me HOW MANY DOGS?

Assuming 15% holds true for the UK then there would be 600,000 dogs in the UK alone BUT perhaps some countries' dogs are more allergic than others.

However, it's apparently a major concern in Cuba
"International veterinary conference on dog population control in Cuba"
http://www.wspa.de/projects/companion-animals/cuba.html

But THIS sounded helpful:
"In six years, one female dog and her offspring can theoretically produce 67,000 dogs. Copyright © 2005 The Humane Society of the United States."
1+67000=67001, hmmm is THAT prime?

"Increased dog density. The dog population in the United States has grown significantly during the last 30 years and is now a large potential reservoir for D. immitis infections. More than a third of all U.S. households own dogs and the current dog population has been estimated as more than 40 million."

So, that's another 40 million dogs for America alone!
http://cal.vet.upenn.edu/merial/hrtworm/hw_3.htm

BUT
"North America has the highest dog population in the world."
http://cal.vet.upenn.edu/merial/hrtworm/hw_3.htm

"We also know India’s dog population doubled in a three year period from 1998 to 2001. Therefore, we can assume Delhi’s dog population also doubled during the same timeframe. " and "At this time, by municipal government estimates, we have approximately 200,000 stray or free roaming dogs in New Delhi. Our own estimates put the number closer to twice that amount or 400,000. "
http://www.animalindiatrust.org/DogControl.html

"the total dog population in the Netherlands is 1.4 million dogs, with 21% of households having a dog."
http://www.achp.health.usyd.edu.au/pets/dogbites.html

"Total number of dogs
1991 3.0mn
1994 3.8mn" for Australia

>According to the Sunday Telegraph, Bramble, living in Bridgewater, Somerset, UK, has just (August 2002) celebrated her 27th birthday, possibly making her the world's oldest living dog and a contender for the "Guiness Book of Records".
How exactly does a dog live to be 189 (in dog years)?
The Daily Mail reports Britain's oldest dog was a pedigree papillon called Fred who died at the of 29 in 2000. The world's longest-lived dog was an Australian cattle dog who lived to be just months older than Fred.

That gives some upper bound on mortality :-)
from http://www.fruitnut.net/index2.htm?PAG=64brambles,REF=

"All over the world, dog population estimates are used to estimate TOTAL DOG POPULATIONS, without which targets for dog control cannot be set."
education.vsnl.com/ecollage/recommend.pdf
>SO, WHAT ARE THEY?

For MERE 100 EUROS I could find out:
"Europe and the US human, pet, and dog and cat population for each of 15 ranked countries or grographic groupings, reported as of July 2000"
http://www.researchandmarkets.com/reports/262885/
That would help me a lot, but its a bit out of date and costs money.

I suppose I'll just have to be content knowing that....

"The current world population of domestic dogs may be as high as 500 million."
http://www.petpeoplesplace.com

500,000,000 = half a billion.

SADLY that's NOT PRIME.

You guys were right all along.

[bearnol]

Originally Posted by jinydu

You misunderstood me there. I was saying that your "proof" is flawed because infinity is not an integer, and there certainly aren't infinitely many integers larger than infinity.

Infinity can be a string of integers (if we're considering an integral infinity). There are infinitely many integers as big as infinity.

Originally Posted by jinydu

You would have to show that for infinitely many Mersenne numbers, Mp, there are no factors larger than the square root of Mp.

For infinitely many Mersenne numbers, Mp is/are infinite. Thus the square root(s) of Mp are also infinite, hence there cannot be any factors larger than the square root(s) of Mp. (though I'm not sure I need this for my proof)

[xilman]

Originally Posted by bearnol

Infinity can be a string of integers (if we're considering an integral infinity). There are infinitely many integers as big as infinity.
For infinitely many Mersenne numbers, Mp is/are infinite. Thus the square root(s) of Mp are also infinite, hence there cannot be any factors larger than the square root(s) of Mp. (though I'm not sure I need this for my proof)

Oh no, not again
Oh well --- Once more unto the breach, dear friends, once more!

Repeat after me: infinity is not an integer. Infinity is the cardinality of the set of integers.

It is meaningless (gibberish, as some may say) to claim that there are any, let alone infinitely many, "integers as big as infinity". Because infinity is not an integer, the relationship "as big as" makes as much sense as "as blue as". How many integers are as blue as infinity?

If you prefer, try looking at it this way: every positive integer, without exception, is finite. Every positive integer is smaller than some other integer. Indeed the cardinality of the set of integers which are larger than any given integer is itself infinite.


Paul

[bearnol]

Hi Paul
(thanks for your response)
I've had exactly this discussion (included, at least) with Will Edgington (as I mentioned above).
You are correct to say that infinity is not _an_ integer. However I am correct to say that infinity can be an (infinite) string of (infinite) integers [at least if we are considering integral infinities]. If we want to continue this discussion, I'll try and look out what I wrote to Will (I kept a record of the development of that discussion) as all of it I will have dealt with before...
J

[bearnol]

Originally Posted by xilman

How many integers are as blue as infinity?

Infinitely many

[bearnol]

Originally Posted by xilman

Indeed the cardinality of the set of integers which are larger than any given integer is itself infinite.

Exactly! (I remember this point from discussion w/ Will)
And since that cardinality must itself be "an" integer (it makes no sense to say the _number_ of integers is non-integral), then they/it must be an/a string of infinite integers, ie there must exist "an" infinite integer to describe that very cardinality

[xilman]

Originally Posted by bearnol

However I am correct to say that infinity can be an (infinite) string of (infinite) integers [at least if we are considering integral infinities].

No, you are not correct. Or, to be precise, your definition of infinity is different from and incompatible with that of mainstream mathematics: in other words, your statement is not correct within the conventional rules of mathematics.

If you are not going to obey the rules of mainstream mathematics, do not be surprised if the vast majority of mathematicians do not take you seriously and do not accept your proof.

Paul

[xilman]

Originally Posted by bearnol

Exactly! (I remember this point from discussion w/ Will)
And since that cardinality must itself be "an" integer (it makes no sense to say the _number_ of integers is non-integral), then they/it must be an/a string of infinite integers, ie there must exist "an" infinite integer to describe that very cardinality

That cardinality itself need not be an integer.

It makes perfect sense (to the vast majority of mathematicians) to say that the number of integers is not itself an integer. All integers are numbers, but not all numbers are integers.

You may, if you wish, take the Humpty-Dumpty defence and use the words "integer", "number" and "infinity" in any way you wish. The consequences of your choice(s) may lead to interesting constructions but unless you choose interpretations demonstrably equivalent to those of mainstream mathematics your results will be theorems only within your own system and need not be theorems of what almost everyone else thinks of mathematics.

Paul

[bearnol]

Personally I am a believer that there is only one absolute Truth.
You seem to be suggesting that mathematical truth depends on the observer?
J

[philmoore]

Originally Posted by bearnol

You seem to be suggesting that mathematical truth depends on the observer?
J

Of course it does! Any kind of "truth" depends upon someone holding it to be true. Where mathematics differs from, say religion or philosophy, is that the nature of mathematical discourse enables people to agree on terms and assumptions in such a way that they can then construct convincing arguments, what we call proofs, and end up in (near-)universal agreement about what statements follow logically from any particular set of assumptions. Your concept of integer is out of the mainstream, and because of that, your mathematical "system", should you develop it as such, will not be equivalent to the one in which most mathematicians work. So there is no reason to expect that a truth in your system will be a truth in another system.