I still don't understand what you are saying.

Also I am not actually talking about primes per se but rather talking about two to the power of any aleph null. Say the integers. I am saying that those combos can be put in an order by using the prime trick. So the combo of the first three integers would be in eight place (because 2x3x5) comes after 6,10,14,15,21,,22, and 26. 2x3x7, the 1st 2nd and 4th member combo would be in 14th place after 30,33,35,38, and 39.

I think you already got that this was what I was saying but your replies are too technical for me to know.

Ok. So let's take the positive integers set as an archetypical aleph null set (call it N). You are saying that I can translate each combo of N in a distinct positive integer. For instance, {1,3,4} -> I get the first (2), the third (5) and the fourth (7) prime number -> multiply them -> get 70. Using that value, I can order and enumerate each combo of N. Is that correct?

Do you agree that the infinite sets:

1 - 4 - 9 - 16 - 25 - ... - n^2 - ...

and

1 - 8 - 27 - n^3 - ...

are both "combos" of N? If so, the "prime number trick" which one rates first? If I follow your rule, for the first I multiply 2 - 7 - and infinite other primes together. Basically the same happens with the second. Both results in an infinite value. Here lies the problem.

The non technical explanation was given in Post 16. Order the list however you want. I went with lowest product to highest product. Once the list is done you can always find a number not on the list by making sure the first digit of the new number is different from the first digit of the first number in the list, second digit is different from the second digit of the 2nd number etc...The new number must be different from every number in the list, so there are more elements to the power set of the integers than the integers.

No. That's not what "uncountable" means. Uncountable means that you cannot create a one-to-one correspondence between the natural numbers and the real numbers.

There is no canonical ordering for countable sets. If I give you a generic countable set, there is no well-defined "next one" that can be defined in some abstract way.

The "prime number trick" doesn't really work because there are subsets that have infinitely many elements in them, and so you don't always get a natural number associated to any set. At least, that's the current best understanding I have of your idea.

All of them seem inaccurate at some level.

I'm rather convinced that he's not actually aware of that.

I believe that the response that directly addresses what I was talking about would be something like "it is not true that different packets of prime numbers multiply out to different products if the packets contain an infinite number of them". If nick in post four had used the word multiply instead of map I would not have been confused.

Isn't basically what I said in post #8?

Glad that the message somehow arrived and sorry for not making myself clearer. Being a non native English speaker I find often very hard to write about maths and science and make myself clear, especially in informal discussions, where technical terms are easily misunderstood.

#8, upon rereading, did in fact do the trick. I would have added a few more words to make the meaning clearer but it was my fault for skimming.

(Most people don't realize how unfamiliar I am with both jargon and mathematical notation. Or conversely, ost mathematicians don't realize that math speak to them is like musical notes to a musician. They hear the song when they read the notes, but few others do.)

Humans consider themselves unique so they've rooted there whole theory of existence on their uniqueness. One is their unit of measure, but it's not. All social systems we've put into place are a mere sketch. One plus one equals two. That's all we've learned, but one plus one has never equaled two. There are, in fact, no numbers and no letters. We've codified our existence to bring it down to human size to make it comprehensible. We've created a scale so that we can forget its unfathomable scale.

A Number is only a constrict of Your mind and there for limited, there are no Numbers . . .

Talking to God...

I met god the other day.
I know what you're thinking. How the hell did you know it was god?

Well, I'll explain as we go along, but basically he convinced me by having all, and I do mean ALL, the answers. Every question I flung at him he batted back with a plausible and satisfactory answer. In the end, it was easier to accept that he was god than otherwise.

-Digital Evolution
Which is odd, because I'm still an atheist and we even agree on that!

http://www.fullmoon.nu/articles/art.php?id=tal

Try to come with profs to say I didn't speak to God . . . Welcome