EFF claim(s)

[Citrix]

Alot of assumptions you make in your proof, can you prove them? Like there were 2 dogs...

[akruppa]

Moved to "Miscellaneous".

Alex

[xilman]

Originally Posted by Numbers

I can’t prove that there are only a finite number of dogs in the universe, but I think I can prove that there are only a finite number of dogs on earth.

Proof deleted.

A much simpler proof, in my opinion of course, follows from the observation that the earth has a finite mass-energy.
A dog, or any organism for that matter, has a finite (i.e., non-zero, non-infinitesimal) finite mass-energy. For all integers a,b (although dogs, and other organisms for that matter, may be real in some sense, they are counted by the integers and not the mathematical reals), a/b is finite.


Paul

[Fusion_power]

Here I try to show the perfect example of a fallacious proof and throw the entire thread off on a tangent.

Xilman, would it also be correct to state that any part of a finite system must of necessity be finite (sum of parts). Since the earth is part of the universe and the universe is a finite system, Earth must be finite. Therefore, anything on the earth is also part of a finite system and must be finite.

My apologies to the originator of this thread, but if even a non-mathematician like me can see the weakness of the proofs cited, they will need some serious work to stand up to a mathematical critique.

Fusion

[xilman]

Originally Posted by Fusion_power

Here I try to show the perfect example of a fallacious proof and throw the entire thread off on a tangent.

Oh dear. That was not my intention.

Originally Posted by Fusion_power

Xilman, would it also be correct to state that any part of a finite system must of necessity be finite (sum of parts). Since the earth is part of the universe and the universe is a finite system, Earth must be finite. Therefore, anything on the earth is also part of a finite system and must be finite.

Nope, that was why I was careful to state non-zero and non-infinitesimal. For instance, the portion of the real number line lying between 0 and 1 inclusive has finite extent but contains an uncountably infinite number of reals and a countably infinite number of rationals.

Further, it is not immediately clear (to me at least) that the universe is finite.

Originally Posted by Fusion_power

My apologies to the originator of this thread, but if even a non-mathematician like me can see the weakness of the proofs cited, they will need some serious work to stand up to a mathematical critique.

Fusion

Unlike your previous statement, that is something with which I agree.


Paul

[xilman]

Originally Posted by xilman

For all integers a,b (although dogs, and other organisms for that matter, may be real in some sense, they are counted by the integers and not the mathematical reals), a/b is finite.

Gah!

I meant, of course, to say that for all integer, a and all non-zero integer b, a/b is finite.


Paul

[Peter Nelson]

First, apologies that we have warped what was originally a serious (albeit misguided) thread, you will see that mathematicians have a unique sense of humour and will expect you to defend your claims rigourously. Don't take it too personally.

Having said that, some observations:

"this is not maths, this is gibberish!" (quoting R Silverman).
Please can you go and READ about dogs before posting in this forum.
Also express your dog algorithm in mathematical language NOT plain english.

You forget to include any additional parallel universes or consider up to 10 dimensions of space.

Also by defining dogs to be animals which are dogs and bitches, you appear to have totally neglected PUPPIES!

We are not talking about all numbers, or even all mersenne numbers but mersenne primes which are rarer. Similarly, personally I am uninterested in Rotweilers and Terriors but love Border Collies as they are extremely intelligent and useful for herding sheep. Therefore I would prefer us to consider the specific case of Border Collies before generalising to other breeds.

I would say that the number of Border Collies (and indeed dogs) on this planet actually COULD be enumerated because we do enumerate the human population which is of a similar order of magnitude.

There is clearly an upper bound on the number of dogs living on the planet because they will not exceed the gross weight of the planet. If there were a large enough number of dogs compressed into the known volume of the planet the gravitational force would cause the dog-planet to collapse in on itself and probably create a black hole.

Barking from such dog-planets would not be able to escape the event horizon so we would not know that such dog-planets exist. Simply because we cannot detect them does not mean one or many such planets do not exist somewhere in the universe.

[Peter Nelson]

More seriously, bearnol,

Look here

http://primes.utm.edu/mersenne/index.html#known

A list of 41 known mersenne primes.

Consider: Can anything in your proof show that there is even ONE more mersenne prime beyond those already found? If so, how?

If your "proof" showed mersenne primes were indeed infinite, it would be a trivial application of this to show there must exist just one more (at least).

Probabalistically we could say we expect to find another around ...... but until we find it we don't know there is one for sure.

[jinydu]

Originally Posted by bearnol

What I'm saying is that since any divisor of Mp, as p->inf, has to be strictly greater than p [actually at least as big as 2kp+1], and since it is impossible to have a number _strictly_ greater than infinity, then there can be no proper divisors of Mp 'at infinity', but instead an infinite string of prime Mp.

The problem here is that infinity is not a number. There is no point at which the smallest possible factor becomes "larger than infinity".

I could use the same reasoning to "prove" that

n! + 1

is prime infinitely often.

[Wacky]

Originally Posted by jinydu

I could use the same reasoning to "prove" that

n! + 1

is prime infinitely often.

Are you claiming that n! +1 is prime for only a finite number of integers, n?

[Peter Nelson]

I conjecture that the total number of dogs is in fact prime.