Re: A Simple Non-Diagonalisable List
- From: "george" <greeneg@xxxxxxxxxx>
- Date: 13 May 2005 12:15:19 -0700
HERC777 wrote:
> Define a class of sets CONTENDER_CLASS as sets
> that have the property
>
> (An, Ec, Ad1, d2 e {0..9}, d1=/=d2, L[n,n]=d1, L[c,c]=d2)
This is meaningless. This is not a class of sets
(unless you are using ZFC and re-encoding EVERYthing
as a set) because "L" is not bound anywhere in this
description. Whatever this is, it is a class of L's,
NOT a class of SETS. If the L's are supposed to be
lists of reals, then IT WOULD'VE HELPED A LOT if you
had SAID that.
See, if you KNEW how to PLAY this game, you WOULD'VE
said something like, "Let's just consider the reals
between 0 and 1, represented as their decimal expansions,
as strings of digits e {0..9}. I think these reals can
be listed, but of course, they can be listed in many different
orders (if you take a list of reals and swap two elements, you
still have a list of reals). Now, some lists of these reals
are complete (they list all the reals between 0 and 1) and
others are not. And some of these lists are CONTENDERS, while
others are not. A list L of reals (where L[x,y] means the y'th
digit of the x'th real on the list) is a CONTENDER if and only
if"
>(An, Ec, Ad1, d2 e {0..9}, d1=/=d2, L[n,n]=d1, L[c,c]=d2)
> L[n,c] = d1 and L[c,n] = d2
And that is mostly mis-spelled as well.
As you wrote it, "Ad1, d2 e {0..9}, d1=/= d2,"
is ALWAYS going ot be false; it simply IS NEVER the
case that For ALL d1,d2e{0..9}, d1 does not equal d2.
In particular, when d1 DOES equal d2, d1 DOES equal d2.
You have GOT to learn how to use brackets right.
What you MEANT was, where w = the natural numbers
and D = the decimal digits {0..9},
AnEcAd1d2[ new & cew & d1eD & d2eD & (d1=/=d2)
-> L[n,n]=d1
& L[c,c]=d2
& L[n,c]=d1
& L[c,n]=d2
]
And you forgot a constraint: just as you requred d1=/=d2,
you also needed to require that c=/=n, since, OBVIOUSLY,
there DOES ALWAYS exist a c satisfying this, namely, c=n.
> Basically we are looking for rows with the diagonal digit repeated
> somewhere, and a corresponding row to swap with.
>
> 0.xxxxxx
> 0.xAxxxA
> 0.xxxxxx
> 0.xxxxxx
> 0.xxxxxx
> 0.xBxxxB
>
>
> There are 2 properties that almost make
> a set CONTENDER_CLASS.
No, that make the LIST, NOT the set a MEMBER of the contender_class.
The contender_class is a set of lists.
Every list in it is a contender. For what, I still don't
know yet.
> 1/ there are oo of every digit contained in every real.
> 2/ the set contains every finite prefix of digits.
Neither one of those has much of ANYthing to do with
being a contender.
> One such list is the random plane in your favorite base.
>
> 0.0102020010222112010..
> 0.0100212120210112120..
> 0.2112202221212120000..
> 0.0000212121000012121..
> 0.1111222010100100001..
You are SUCH an idiot, Herc.
THERE IS NO SUCH THING as "the random plane".
There are a GREAT MANY DIFFERENT planes, NONE MORE
NOR LESS random (pace Chaitin and Kolmogorov)
than ANY other! RANDOMness is a property
of HOW SOMETHING WAS GENERATED, of what STRATEGY (or lack
thereof) you used in putting pegs into the holes! ONCE YOU
KNOW all the pegs, NOTHING about the situation is random!
I could roll a pair of fair dice, but whatEVER number may
come up, that zNUMBER is NOT random! "7" is NOT any more
or less "random" then 2,3,4,5,6,8,9,10,11,12,1,42, or 69!
THEY ARE ALL *just* numbers!
.
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