Re: A Simple Non-Diagonalisable List


HERC777 wrote:
> AnEcAd1d2[ new & cew & d1eD & d2eD & (d1=/=d2)
> -> L[n,n]=d1
> & L[c,c]=d2
> & L[n,c]=d1
> & L[c,n]=d2
> ] ]
>
>
> to me that says, for all digits, L[n,n] = that digit.

Well, yeah, I was trying to paraphrase you,
so of course I didn't get it right.
You don't know how to speak math and
I don't know what you are trying to say,
so between the two of us, it is bound to stay
wrong for a while.

I think what you meant was that for every real on
the list, you want there to be SOME other real on the list
that you could swap it with without changing the diagonal.

In that case, you need
> AnEcd1d2[ new & cew & d1eD & d2eD & (d1=/=d2)
> -> L[n,n]=d1
> & L[c,c]=d2
> & L[n,c]=d1
> & L[c,n]=d2
> ] ]

i.e., d1 and d2 don't really need to be quantified
at all because they are totally dependent on n and c
(d1 is L[n,n] and d2 is L[c,c]). You really
only introduced d1 and d2 as abbreviations, so you
could say the other constraints shorter.
Without that irrelevance, WHAT YOU MEANT
was (probably)

AnEc[ L[n,c] = L[n,n]
& L[n,n]=/= L[n,c]
& L[c,n] = L[c,c]
]

> that's why I had L[n,n]=d1 as a condition,
> not anything implied.

You CAN'T DO conditions THAT way. you wrote:

> (An, Ec, Ad1, d2 e {0..9}, d1=/=d2, L[n,n]=d1, L[c,c]=d2)

As a condition, and I'm sorry, that's JUST NOT grammatical.
Not until AFTER you define a programming language that
does in fact do them that way. Around here, you DON'T GET
to say "for all d1 and d2 such that d1 =/= d2".
That's not even what you meant to say anyway.
That's 90 different combinations of d1 and d2 and you can't
mean to allege that all 90 of them are relevant to every
real on the list. Some reals on the list represent
x/9 for some x and therefore only have ONE d occurring
in the whole real! The way you would ACTUALLY write
what you were TRYING to say here is
AnEc[ L[n,n]=/=L[c,c]
& whatever ]

> I will add c>n anyway

You can't "add" ANYthing to THIS (as you have written
it) because THIS is incoherent gibberish! You have GOT
to agree to speak the SAME programming language
as the people READING!

> I need this quality later when the 'blind shuffle'
> operation is demonstrated.

I don't know why the *** you are trying to talk about
"blind shuffling" down here in the post, when THE SUBJECT
says this is supposed to be about a list that is "non-
diagonalizable".
No amount of shuffling is EVER going to get you a list
that can't be diagonalized. For ANY L whatsofUCKINGever,
D[x]= 9-L[x,x] is an anti-diagonal of L and there is
JUST NOTHING that YOU can EVER do about it. Not
randomizing, not shuffling, not calling Cantor stupid,
NOT NOTHIN'.

.

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