Introducing the WIDTH of a REAL NUMBER! >>>>|<<<<

Graham Cooper

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May 20, 2012, 4:51:37 AM5/20/12

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On May 20, 6:27 pm, netzweltler <reinhard_fisc...@arcor.de> wrote:
> What does 2 x 2 x 2 x 2 x ... mean?
> Is it like 2 + 2 + 4 + 8 + 16 + ...?

Cantor defined it as 2^aleph_0
the amount of infinite binary strings

> What about
> 0.5^oo <- Is this term even well-defined?

It's infinitely small but not in any x->oo 1/x way!
If you multiplied it by |R| you should get 1 though!

Herc
--
"How lucky we are to be able to hear how miserable Willie Nelson
could
imagine himself to be." -- Ken Tucker on Fresh Air

netzweltler

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May 20, 2012, 6:10:33 AM5/20/12

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On 20 Mai, 10:51, Graham Cooper <grahamcoop...@gmail.com> wrote:
> On May 20, 6:27 pm, netzweltler <reinhard_fisc...@arcor.de> wrote:
>
> > What does 2 x 2 x 2 x 2 x ... mean?
> > Is it like 2 + 2 + 4 + 8 + 16 + ...?
>
> Cantor defined it as 2^aleph_0
> the amount of infinite binary strings

I know that the cartesian product {0, 1} x {0, 1} x {0, 1} x ...
results in the set of all infinite binary strings. The resulting set
is {0, 1}^N, {0, 1}^w, or {0, 1}^aleph_0. A short form is also 2^N.
Does this mean that

2 x 2 x 2 x ... = 2^N = 2^w = 2^aleph_0

does make any sense?

> > What about
> > 0.5^oo <- Is this term even well-defined?
>
> It's infinitely small but not in any x->oo 1/x way!
> If you multiplied it by |R| you should get 1 though!

Is "infinitely small" well-defined?

> Herc
> --
> "How lucky we are to be able to hear how miserable Willie Nelson
> could
> imagine himself to be." -- Ken Tucker on Fresh Air

--
netzweltler

Graham Cooper

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May 20, 2012, 6:12:38 PM5/20/12

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On May 20, 8:10 pm, netzweltler <reinhard_fisc...@arcor.de> wrote:
> On 20 Mai, 10:51, Graham Cooper <grahamcoop...@gmail.com> wrote:
>
> > On May 20, 6:27 pm, netzweltler <reinhard_fisc...@arcor.de> wrote:
>
> > > What does 2 x 2 x 2 x 2 x ... mean?
> > > Is it like 2 + 2 + 4 + 8 + 16 + ...?
>
> > Cantor defined it as 2^aleph_0
> > the amount of infinite binary strings
>
> I know that the cartesian product {0, 1} x {0, 1} x {0, 1} x ...
> results in the set of all infinite binary strings. The resulting set
> is {0, 1}^N, {0, 1}^w, or {0, 1}^aleph_0. A short form is also 2^N.
> Does this mean that
>
> 2 x 2 x 2 x ... = 2^N = 2^w = 2^aleph_0
>
> does make any sense?
>
> > > What about
> > > 0.5^oo <- Is this term even well-defined?
>
> > It's infinitely small but not in any x->oo 1/x way!
> > If you multiplied it by |R| you should get 1 though!
>
> Is "infinitely small" well-defined?
>

Let's call
oo = |N|

and
|N| = aleph_0

then
2^aleph_0 *1/2^aleph_0 = 1^aleph_0 = 1

So
aleph_1 * 1/2^|N| = 1

|R| * 1/2^|N| = WIDTH OF [0,1]

1 UNIT WIDTH / COUNT(REALS) = 1/2^|N|

but but but..... I don't care what Cantor said.... SAY WHEN!
What line in my post do you disagree with? THEN make your point!

Herc

netzweltler

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May 21, 2012, 12:54:10 PM5/21/12

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To me it looks like you are treating aleph_0 like a very big natural
or real number. I'd disagree with that. Furthermore I don't get what
"infinitely small" could mean other than 0. If it is greater than 0
then I'd call it "finitely small", because there is no small number >
0 which is not a real number, is it?

--
netzweltler

Graham Cooper

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May 23, 2012, 3:33:04 AM5/23/12

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finitely small would be lim x->oo 1/x

1 UNIT WIDTH / COUNT(REALS) = 1/2^|N|

This is the standard way to calculate width (of Reals)

by YOUR Theory that cannot be finite.

2X2X2X.. is just ->oo

in MY WORLD, NORMAL GOOD OLE CALCULUS

and anybody who says Stratifying the *FORMULA*

DIGIT-STRING = NOT-ALL-OTHER-NUMBERS(DIGITS) is unnecessary.

You wouldn't call AD(N2NPERMUTATION(DIGITPOS)) a missing row?

xxOxx..
xxxOx..
Oxxxx..
xOxxx..
xxxxO..
..

So why do you call AD(X=Y(DIGITPOS)) a missing row?

Oxxxx..
xOxxx..
xxOxx..
xxxOx..
xxxxO..
..

Herc
--

TM-SIZE MAX-1s OUTPUT
-------------------------
BB(2) 6
BB(3) 38
BB(4) 3,932,964
BB(5) 1.7 x 10^352
BB(6) 1.9 x 10^4933
...
BB(199) COOPERS NUMBER
BB(200) UNIVERSAL TURING MACHINE SIZE
includes PorkyPig Jnr's Number = CN+1

Graham Cooper

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May 23, 2012, 3:44:08 AM5/23/12

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On May 23, 5:33 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
>
> finitely small would be lim x->oo 1/x
>

x->oo 1/x

not the limit which is just 0.

Herc

netzweltler

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May 23, 2012, 3:14:05 PM5/23/12

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To complete the set of binary sequences of the 3x3 list

100
010
001

the missing sequences are

000
110
101
011
111

and the AD is one of these sequences.
To complete the set of binary sequences of the 4x4 list

1000
0100
0010
0001

the missing sequences are

0000
1100
1010
0110
1110
1001
0101
1101
0011
1011
0111
1111

and the AD is one of these sequences.
To complete the set of binary sequences of an (infinite)x(infinite)
list there are plenty of missing sequences
and the AD is one of these sequences.

--
netzweltler

Graham Cooper

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May 23, 2012, 4:12:13 PM5/23/12

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Yes! That's called a THEORY!

What sci.math is is a MOB! Like anti-bodies rejecting a new limb!

Herc

Graham Cooper

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May 23, 2012, 4:55:04 PM5/23/12

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Here's the first 11x10 digits of an NxN list!

0123456789...
9876543210
2468097531
1357989426
3012674859
4201365978
8940123567
7394210645
5732801092
6585332103
0679768324
...

According your set of ANTI-DIAGONALS where the permutation function
n2n is unbound giving a set of results.

AD(pos) = change (LIST(n2n(pos),pos))

3141592653.. is missing
1414213562.. is missing
2718281828.. is missing

NO PI FOR YOU!

0123 [4] 56789...
987654 [1] 210
[2] 469097531
13578 [8] 9426
3 [0] 12674859
4201365 [5] 78
894 [0] 123567
739421062 [2]
57 [3] 2802095
6585331103
06797683 [4] 4
...

the possible diagonal [2][0][3][0][4][8][1][5][4][2]...

gives AD 3141592653...

If you're suggesting this method shows PI is missing if extrapolated
that's one thing!

If you're suggesting THAT then proves |R| > oo that's another!

netzweltler

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May 24, 2012, 1:49:55 AM5/24/12

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To get an idea of how much more missing binary sequences there are
compared to the natural numbers I would list the sequences of the
natural numbers

(0) 000000...
(1) 100000...
(2) 010000...
(3) 110000...
(4) 001000...
...

Here we can see that every row consists of infinitely many 0's and
only finitely many 1's. You would say, the number of 1's
is infinitely small compared to the number of 0's (I would say, the
number of 1's is 0% of all bits in a row). So, even if there is an
infinite number of 1's in the list, this number is not more than 0% of
the number of all bits in the list.

--
netzweltler

Graham Cooper

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May 24, 2012, 3:50:38 AM5/24/12

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This is where the argument goes in circles.

In the matherealists UoD where every set or real has a formula from a
small finite alphabet string of characters, your view is inconsistent.

By starting with "->oo" in Calculus and adding "oo->" in Cardinality
you all have a contradiction in your system which means YOU, as in
PEOPLE can output any false theorem at all. Nothing you say can be
trusted.

SCI.MATH |- ->oo
SCI.MATH |- oo->

You'are all inconsistent, in every sense of the term.

You just ignored the fact I proved PI is missing from a list of reals!

If you want to argue with me, please read www.MATHEOLOGY.com first and
do the example programs. EVERY LINK PLEASE, I didn't make 10,000
posts on the topic for fun.

Herc