My “argument” has nothing to do with the rationals.
Why? Are you having trouble understanding them?
Nothing until you apply it to an infinite set.
Completely irrelevant (not to mention a bit childish).
Let’s step back here…
1.) rationals have terminating or terminating through repeating
2.) we have already ordered 1
3.) the issue with the reals, is that the irrationals are non terminating non terminating through repetition
4.) we haven’t sequenced the irrationals yet
So the issue here is that James believes that it’s been proven that 4 can’t be sequenced…
We know how to make lists of 4.
As I discovered in the technique of dimensional flooding, when each unit on an infinite list has another infinite list then something I called dimensional flooding occurs. Which means you have to make a new list.
Now, perhaps James is correct, I don’t think so, but he might be correct that irrationals cannot be sequenced.
However, his argument is circular in the sense that the conclusion is the premise.
He adds the reals between the wholes and states that there are infinitely more in between, and to use my terminology, since this causes dimensional flooding, the reals cannot be listed by the wholes.
What wtf pointed out then, was that there are an infinite number of rationals between each whole as well, which in my terminology should also cause dimensional flooding, but we use an additional operator to interpolate with the other operator to make an ordered rational list that we know counts the entire sequence, but it’s not well ordered!
So, wtf, said that James analogy falls apart to this regard !
So it’s encumbant upon James at this point, to offer a proof that the situation is specifically completely different for non terminating / non repeating sequences, and that it’s not just a matter that we haven’t discovered the interpolation for them yet!
There’s my summary, that’s where we are.
Exactly right. James’s argument that the set of reals is larger than the set of integers also shows that the set of rationals is larger than the set of integers. But we can easily fit the set of rationals inside the set of integers with plenty of integers left over. So James’s proof is “too strong,” in the sense that it proves something known to be false. That shows that James’s proof is wrong; or at the very least, in need of refinement.
Wtf, with everything I know about this topic, none of it taught me, I am basically looking for “ecmandu’s operator” like the boson is named after Higgs …
It’s all about operators and sequence…
Anytime a new operator is added, the list ceases to be well ordered, but it can still be ordered, the operators are finite… So I see no reason why the reals can’t be listed in a single list!!
Why be so boring right wtf!!!???
So I’ll tell you what I think my operator is!
0123456789
1234567891
2345678910
3456789101
Then you run a diagonal for every digit in this sequence…
It’s actually deceptively simple!!
I can do an inferential proof… But I’m not smart enough to tell you where pi is yet…!!!
I don’t follow this at all.
First, each row is a finite sequence of digits. In fact they’re all exactly 10 digits long if I counted correctly. There are only finitely many of those and so even if you take every possible antidiagonal you can only generate finitely many new sequences, each of which will be finite.
Also I don’t see the pattern. The second row is missing 0 and has two 1’s. How are you getting these sequences?
On the other hand if you mean to imply “…” dots at the end, please include them because this is an extremely important point of notation. It lets everyone know what you’re talking about.
Secondly even if the strings are infinite you will run into the problem of Cantor diagonalization which will yield a sequence that can not possibly be on your list, no matter what the list.
On a totally different topic – ignore all this if it’s off the mark – I want to check something with you. A sequence by definition is countable. It is not possible to sequence the reals.
However it IS possible to well-order the reals. This is a technical topic and if I explained myself I’d be guilty of being longwinded again. You got me there 
Long story short, I just want to make sure you’re not trying to well-order the reals as opposed to sequencing them. Because assuming a principle of set theory known as the axiom of choice, you can well-order any set whatsoever.
But any well-ordering of the reals (a) Can’t possibly be described; (b) certainly can’t be visualized; and (c) is not a sequence, because the reals are uncountable.
I was being brief… sigh apologies…
00
-0, -0
Just let this be implied for the grid…
The grid for the 4 quadrants has each of this sequence!!!
012345678910… (Infinite counting up)
123456789101…
234567891011…
345678910111…
456789101112…
567891011121…
… ( this list goes on forever )…
In 4 quadrants !!!
EACH!!! Place in this quadrant sequence, diagonalized in 4 directions for EVERY place in the sequence will count the reals!!!
That’s more clear. You have an infinite list of infinite sequences. Ok. But I still don’t see how you generate the sequences.
I thought I had a clue looking at the columns. The first column is 012345… (writing a column in your list all on one line here).
The second column is 12345… The third column is 23456… So I thought, AHA I understand. But the pattern soon breaks down. For example you have a column 891011. Where did that come from?
Ahh!!! You don’t get the sequence!!!
You can use it to count the reals!!!
It’s the decimal expansion of the number:
12345678910111213141516171819202122232425…
Etc… And then marched in for each line…
There’s actually a name for this number , but I forgot … And I’m drunk, I’ll reply later !!
Oh I see what you’re doing.
So later in the list you have
8901234567891011…
91011121314151617…
01234 … uh-oh it looks like you are cycling back to the beginning here. Help me out. I’ve got the main point of your idea but I don’t see what happens when the first digit cycles.
Oh wait … afer 9 would be 10? So after
8901234567891011…
91011121314151617…
we have
101112131415…
111213141516…
and so forth?
Tell me if I have that right.
Now of course this can’t possibly help because of the Cantor diagonal argument, which applies to any possible list.
But at least confirm that I understand your pattern correctly.
These are diagonals from that sequence!!!
The thing about cantor, it’s amazing he discovered irrationals can be made from diagonals!
I’m using diagonals from my set to make the irrationals!!
As you’re marching in the lines… You’re also doing diagonals from each single place!!
In all 4 directions!!
Diagonals are actually easy to list…
And of course you know there are sets where the diagonal is and isn’t a member…
I wish I could just talk to you on my porch for an hour!
True.
No, you cannot.
No. It proves simply something that you confuse yourself through improper rhetoric to be false, like you saying that “infinity / infinity = 3 proves that infinity is equal to 3/1”.
I gave a simple demonstration earlier, based on the prime factorization theorem known to Euclid.
If you have a specific concern with the proof, please explain your reasoning.
To the extent that you refuse to follow a simple mathematical proof accessible to a high school student without providing sound reasons, you are not arguing in good faith.
James doesn’t understand…
Check this out wtf!!!
…
…312111019876543 : 34567891011121…
…121110198765432 : 23456789101112…
…211101987654321 : 12345678910111…
…111019876543210 : 01234567891011…
…111019876543210 : 012345678910111
…211101987654321 : 123456789101112…
…121110198765432 : 234567891011121…
…312111019876543 : 345678910111213…
…
You gave a false and misleading demonstration.
I did. Such efforts do not apply to infinite sets, primarily because they have no end so you can never say that you applied it to the entire set. You asked a question midst the demonstration. You didn’t wait for my answer, but presumed that I agreed. I did not agree.
Quite the opposite. Even you saw that the proof that I gave was simple and to the point. You attempted to throw in a confounding element to try to obfuscate a counter point.
Clear simplicity overrules obfuscated complexity.
Save me a beer!
But no matter how long we talk, Cantor’s diagonal argument will still apply and every possible list of sequences, no matter how it’s generated, cannot contain all possible sequences. That’s simply not going to change no matter how you choose the sequences on your list.
Each rational is coded by a pair of integers. It’s easy to code pairs of integers as a single integer. You just encode (n,m) as 2^n x 3^m. The encoding is uniquely reversible. There is absolutely no infinitary reasoning in this. On the contrary, it’s a finite coding problem. You give me a pair of integers, I give you back an integer. You give me that integer, I give you back your original pair of integers.
I just saw this. It’s very clear and also very easy to explain why it’s wrong.
You are only considering bitstrings (or decimal sequences) that can be generated by an algorithm. I absolutely agree with you that there are only countably many of those.
However, you are not accounting for the uncountably many random bitstrings. Sequences of 0’s and 1’s that have no pattern; that are not generated by any algorithm; and that cannot be characterized, described, or generated by any finite string representing an algorithm.
If you want to make the claim that the computable reals are countable, you’ll get no argument from me. On the contrary, the proof is easy. There are only countably many algorithms, because an algorithm is a finite bitstring and there are only countably many finite bitstrings.
You’re simply ignoring all the non-computable reals.
All you have to do for diagonalization, is list the diagonal, and then the diagonal to the right and the left. Etc…
wtf , I’d give you a braingasm in an hour of talk !!
Lol