:)

I used to think it was impossible to order the reals, but I just figured it out.

I used the technique I “invented / discovered” for counting the rationals, and used a feedback loop on the list using the same algorithm in listed dimensions counting up to infinity.

I may post it… I’m trying to decide what to do with it.

Additionally, not only do I know how to list every combination of number, I know how to list all of the combinations of spaces between all the combinations of numbers

; )

Basically, I looked at cantors grid for about an hour today, building on the mirroring technique I already discovered … And it hit me, I can use every combination of rationals to run a complete set of diagonal reals. I can prove every combination must be there … It’s ordered, but not “well ordered”.

I’m keeping how I solved it personal for now.

That’s just a clue.

This cannot even be done on a quantum computer and so for a human being it is just impossible
For it would take longer than all of infinity to isolate a single space between any two irrationals
The space in question does not actually exist for it will always be occupied by another irrational

I’m not saying I can do it in a single line, nor did I ever imply that.

Let me be clearer… When I say “all the combinations” I don’t mean ALL combinations… You can’t even order the natural numbers with ALL
Combinations… I mean simply that I know how to order them, that was misleading… Apologies

Apologies, that was misleading … Here’s more on that issue… I didn’t mean to make the claim that way!!

For example:

One combination is

01

Another is

10

You can’t start with both numbers on the same line , duh!!!

The only way you can list entire infinite sequences that have multiple combinations is to use multiple lines with the counting numbers, since one has to be first to begin enumerating the sequence, it is impossible to make all of them first, infinite sequencing with parallel processing doesn’t have an end, so technically the processing cannot even begin.

How do you start parallel processing all the counting numbers, when there is no last one… That’s just working the problem in terms of all combinations (that every member of the sequence can be the first one) when it’s linear instead of parallel the problem is much more obvious.

This is actually an important topic you raised surreptitious!!!

I was convinced that to enumerate the reals in order, that you had to parallel process an entire infinity to prove the complete set… Then I ignored the problem for a few years and came back to it today with a fresh insight …

An infinite set can not have every number or quantity within that set specifically listed for it would take
forever to do that. So for example 3 is part of the infinite set of odd integers but if one had to list all of
the ones in this set it could not be done. When you add irrationals then the infinity increases even more

By the way the first number in a sequence with only 0 and 1 in it after 0 itself would not be 01 but an infinity of 0 with 1 at the end
However since that cannot be expressed because infinity is never ending then it would have to be a finite number of 0 followed by 1
But no matter how many 0 there were one could always add another 0 so you would not even have the first number in this sequence
Less you limited that to the number of places each number had so for example 0 then 1 then 01 then 10 then 11 and so on and so on

Whatever,

When someone says 0123456789101112…

They don’t need an infinite number of zeroes at the beginning, and it’s an inferential proof of what the string is… You show that you do know what you’re tLking about and don’t .