Baffling Thread

Question:
There are less even numbers (2, 4, 6, 8...) then there are counting numbers (1, 2, 3, 4...) correct?

Greg

Correct.

incorrect

numbers are infinite
so you can't define the amount of even or counting numbers there are...

the only time that above statement is correct is when you have defined a range, say 1 to 100

but you are missing every second number? but then again i guess numbers are infinate so i'll just ignore this discussion to avoid looking like a f00l

Numbers are indeed infinite, but as INtense! pointed out, you are missing every second number, so there are less of them! Now, how can something be less infinite?

Think about it...tis well baffling indeed!!

liquid

Greg

hmm....

2,4,6,8,10,12,14,16,18
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18

No matter what, even if they are infinite theres always more normal numbers than even numbers.

^he does have a point

Well, apparently this puzzled mathematicians for friggen ages. They didn't know how to define infinity and they couldn't imagine that something which is undeniably smaller than an infinite quanitity is also infinite.

Fermat's wrote:
To resolve the paradox of the infinite it is necessary to define what is meant by infinity. Georg Cantor, who worked alongside Hilbert, defined infinity as the size of the never-ending list of counting numbers (1, 2, 3, 4,...). Consequently anything which is comparable in size is equally infinite.

By this definition the number of even counting number, which would intuitively appear to be smaller, is also infinite. It is easy to demonstrate that the quantity of counting numbers and the quantity of even numbers are comparable because we can pair off each counting number with a corresponding even number:

1 2 3 4 5  6  7
| | | | |  |  |
2 4 6 8 10 12 14

If every member of the counting numbers list can be matched up with a member of the even numbers list then the two lists must be the same size. This method of comparison leads to some surprising conclusions, including the fact that there are an infinite number of primes.

That's from a book I'm reading, Fermat's Last Theorem, by Simon Singh. It's friggen facsinating!! I'm about half-way through it at the moment.

liquid

Greg

- Edited By liquid On Sun 3rd, Nov 2002 @ 9:05:08am

By this definition the number of even counting number, which would intuitively appear to be smaller, is also infinite.

That's what i would have said. How can you put a specific number on infinity divided by 2? Is it half of infinity? What is half of infinity? You can't have that, thus i reckon half of infinity is infinity.

Logically you would imagine that even numbers would be less than counting numbers as Azzor suggested, but seeing as you can't decisively put an exact number on infinity, you can't make that assumption.

This is one problem for the vaults never to be officially solved. Much more important things in life than to be worrying about these things, but they are quite thought-provoking if you ask me.

M@t wrote:

By this definition the number of even counting number, which would intuitively appear to be smaller, is also infinite.

That's what i would have said. How can you put a specific number on infinity divided by 2? Is it half of infinity? What is half of infinity? You can't have that, thus i reckon half of infinity is infinity.

Logically you would imagine that even numbers would be less than counting numbers as Azzor suggested, but seeing as you can't decisively put an exact number on infinity, you can't make that assumption.

This is one problem for the vaults never to be officially solved. Much more important things in life than to be worrying about these things, but they are quite thought-provoking if you ask me.

Maybe a proper way of answering this would be

'There are NOT less even numbers than counting numbers...
There are NOT the same amount of even numbers and counting numbers...
There are NOT more even numbers than counting numbers...'

Hmm. Baffling indeed. Infinity is a strange thing.

/me is confused

*me is also

//me thinks its time to jump on the bandwagon

well actually, there is more counting numbers...

due to the fact that the highest number countable is a googleplex.

so really there are more countable numbers.
since there would only half of a googleplex for even numbers.

Another Annoying Question:
Which came first; the Chicken or the Egg?

- Edited By tw13ve On Mon 4th, Nov 2002 @ 8:40:10pm

I refer you back to my previous statement, and also that since infinity is not a definable number, infinity / 2 is still infinity, i do believe it is universally accepted that this is correct.
This is an important factor when calculating mathematical series (and limits), as it is defined that (contrary to popular belief), infinity / infinity is not 1, it is in fact undefined.

Therefore, any mention of an "amount" of a certain type of number is incorrect when dealing with an infinite range, as no matter what, it is infinity.

And as to the egg/chicken question

The egg. It would have been a genetic mutation in the egg of another species of animal that spawned what we know now as a chicken.

tw13ve wrote: well actually, there is more counting numbers...

due to the fact that the highest number countable is a googleplex.

so really there are more countable numbers.
since there would only half of a googleplex for even numbers.

- Edited By tw13ve On Mon 4th, Nov 2002 @ 8:40:10pm

Actually no, the highest countable number is a FNARP, which is :

6 * 10 ^ googleplex

Jedi-Dave wrote: I refer you back to my previous statement, and also that since infinity is not a definable number, infinity / 2 is still infinity, i do believe it is universally accepted that this is correct.
This is an important factor when calculating mathematical series (and limits), as it is defined that (contrary to popular belief), infinity / infinity is not 1, it is in fact undefined.

This is what I recall from all the maths courses I ever took, i.e. if you accept infinity as an unatainable number... you cannot meaningfully divide it in half.

I think in calculus there's some weird stuff for limits for 1/infinity being almost 0 or something weird.. but it's not EQUAL to.. same idea for infinity/infinity.

And as to the egg/chicken question

The egg. It would have been a genetic mutation in the egg of another species of animal that spawned what we know now as a chicken.

True, unless you're approaching it from a creationist perspective, which some early thinkers may have been (or certainly before evolution was formalized by Darwin).

Then it's unanswerable

Cool thread.

i give up, it gets too confusing..

FNARP!? never heard of that, well now i do, insane.

1/infinity is not techincally a defined value

however the limit of 1/x as x approaches infinity is EQUAL to 0;

inifinity/inifinity is not a defined value either. When using the ratio test for calculating limits of a function, you may come across equating the limit of inifinity/infinity, however in this case it is undefined, and thus you must use a differnet method to calculate the limit.

Back to the egg/chicken question, you're right i'm looking at a scientific perspective. If it was based on creationist, wouldn't it be the chicken? Since from what i remember from R.E. god created 'man' and 'woman' first rather then children. i.e.the equipment and the capability to reproduce was created first, rather then the reproducing process

but this is chickens!! CHICKENS!!!

and the answer is, they both came at the same time; one inside the other.

tw13ve wrote: but this is chickens!! CHICKENS!!!

and the answer is, they both came at the same time; one inside the other.

No you are wrong.

Technically, the scenario you have described is one which in human terms would be deemed as a "gay" relationship. A "chicken" as you describe is of feminine gender. thus it would be impossible for two "females" to be able to reproduce without the aid of scientific measures and even then, a "male" influence would be necessary. The key element you are missing from your theory is the "rooster", or as is otherwise known, the "male" chicken.

And to bring this thread back to its original topic, I reckon Dave is some super-maths-king. Cos he's raking out these mumbo-jumbo mathematical theories and analyses. He certainly is one "scary" individual

Actually its just 1st year University Maths.
I'm only did it cause I have to.
Doing 2nd year Uni maths atm, now that is scary.

Oh and your right about the whole gay chicken thing

Unless of course the first few chickens were asexual... don't ask me how then the normal chicken came along, cause I'm sticking with my genetic mutation answer

gay chickens :o
isnt fermat's last thereom unproven still? i think i remember reading that he wrote it down on his bed sheets as he was dying, then died before he could explain it, and has yet to be proven or disproven (i think they have like 5 crays workin on it at this very moment)

which theorem might that be?