On Saturday, 12 February 2022 at 04:55:30 UTC-4, WM wrote:
[...]
> If the number of lines does not change, then the elements of |N cannot change and then number of O's in
>
> OXXX...
> OXXX...
> OXXX...
> OXXX...
> ...
>
> cannot change either. But Cantor claims that the O's can cover all X. Contradiction.
> 1/1, 1/2, 1/3, 1/4, ...
> 2/1, 2/2, 2/3, 2/4, ...
> 3/1, 3/2, 3/3, 3/4, ...
> 4/1, 4/2, 4/3, 4/4, ...
> 5/1, 5/2, 5/3, 5/4, ...
> ...

Your usual bullshit. No matter how nicely you try to package it, it is still bullshit, and it STINKS. You think that saying over and other "Cantor is wrong" proves anything. The only thing it proves is that you have NO CLUE about mathematics. (But you have demonstrated that for at least fourteen years, so one should not be surprised.)

On 2/12/2022 3:15 AM, Chris M. Thomasson wrote:
> On 2/12/2022 1:13 AM, Chris M. Thomasson wrote:
>> On 1/19/2022 8:24 PM, sergio wrote:
>>> On 1/19/2022 4:24 PM, WM wrote:
>>>> William schrieb am Mittwoch, 19. Januar 2022 um 21:24:37 UTC+1:
>>>>> On Wednesday, January 19, 2022 at 2:32:18 PM UTC-4, WM wrote:
>>>>>> William schrieb am Mittwoch, 19. Januar 2022 um 16:06:05 UTC+1:
>>>>>>> On Wednesday, January 19, 2022 at 5:25:44 AM UTC-4, WM wrote:
>>>>>>>> William schrieb am Mittwoch, 19. Januar 2022 um 00:39:06 UTC+1:
>>>>>>>>> On Tuesday, January 18, 2022 at 6:08:45 PM UTC-4, WM wrote:
>>>>>>>>
>>>>>>>>>>>> But ℵo FISONs are not available because of the pigeon hole principle. You cannot distinguish more strings of o's
>>>>>>>>>>>>
>>>>>>>>>>>> o
>>>>>>>>>>>> oo
>>>>>>>>>>>> ooo
>>>>>>>>>>>> ...
>>>>>>>>>>>>
>>>>>>>>>>>> than are o's avaible.
>>>>>>>>>>> Agreed. There are aleph_0 lines, Thus there are aleph_0 o's available.
>>>>>>>>>> FISONs have less than aleph_0 o's.
>>>>>>>>> Nothing you can say will change the fact that here are aleph_0 lines. Thus there are aleph_0 o's available.
>>>>>>>> OK, if you believe in infinite FISONs,
>>>>>>> Nope. I do not believe in an infinite FISON. Each line is finite.
>>>>>> Each line is the union of all preceding lines + o.
>>>>> Correct. Does not, nothing you say can, change the fact that there are an infinite number of lines.
>>>>
>>>> An infinite number of finite lines. That implies that the infinity is potential.
>>>
>>> nope. there are 2 dimensions to it, one is finite, the other is infinite.
>>
>> Both dimensions are infinite wrt iteration... Think of something along the lines of:
>>
>> [0] = 0/1, 0/2, 0/...n
>> [1] = 1/1, 1/2, 1/...n
>> [2] = 2/1, 2/2, 2/...n
>> [3] = 3/1, 3/2, 3/...n
>>
>> [...]
>>
>> Humm...
>>
>
> think of Cantor Pairing creating an infinite number of single numbers from two numbers, and vise versa.
>

current topic is 2D to 1D mappings, but Im sure it can be extended to 3D to 1D mappings, (done in streaming digital TV) and why not nD to 1D ?

For an n dimentional structure we have all the info on the indexes already, so it is a matter of serializing it.

that puts Cantors Enumeration in with the baby steps.

sergio wrote:

>> think of Cantor Pairing creating an infinite number of single numbers
>> from two numbers, and vise versa.
>
> current topic is 2D to 1D mappings, but Im sure it can be extended to 3D
> to 1D mappings, (done in streaming digital TV) and why not nD to 1D ?
> For an n dimentional structure we have all the info on the indexes
> already, so it is a matter of serializing it.

MASSIVE 50 MILLION C0VID VACCINES RECALLED AS THEY TRIGGER POSITIVES IN
HIV TESTS

On 2/12/2022 12:21 PM, Darrel Angus wrote:
> sergio wrote:
>
>>> think of Cantor Pairing creating an infinite number of single numbers
>>> from two numbers, and vise versa.
>>
>> current topic is 2D to 1D mappings, but Im sure it can be extended to 3D
>> to 1D mappings, (done in streaming digital TV) and why not nD to 1D ?
>> For an n dimentional structure we have all the info on the indexes
>> already, so it is a matter of serializing it.
>
> MASSIVE 50 MILLION C0VID VACCINES RECALLED AS THEY TRIGGER POSITIVES IN
> HIV TESTS

population control

On 2/12/2022 7:08 AM, sergio wrote:
> On 2/12/2022 3:15 AM, Chris M. Thomasson wrote:
>> On 2/12/2022 1:13 AM, Chris M. Thomasson wrote:
>>> On 1/19/2022 8:24 PM, sergio wrote:
>>>> On 1/19/2022 4:24 PM, WM wrote:
>>>>> William schrieb am Mittwoch, 19. Januar 2022 um 21:24:37 UTC+1:
>>>>>> On Wednesday, January 19, 2022 at 2:32:18 PM UTC-4, WM wrote:
>>>>>>> William schrieb am Mittwoch, 19. Januar 2022 um 16:06:05 UTC+1:
>>>>>>>> On Wednesday, January 19, 2022 at 5:25:44 AM UTC-4, WM wrote:
>>>>>>>>> William schrieb am Mittwoch, 19. Januar 2022 um 00:39:06 UTC+1:
>>>>>>>>>> On Tuesday, January 18, 2022 at 6:08:45 PM UTC-4, WM wrote:
>>>>>>>>>
>>>>>>>>>>>>> But ℵo FISONs are not available because of the pigeon hole
>>>>>>>>>>>>> principle. You cannot distinguish more strings of o's
>>>>>>>>>>>>>
>>>>>>>>>>>>> o
>>>>>>>>>>>>> oo
>>>>>>>>>>>>> ooo
>>>>>>>>>>>>> ...
>>>>>>>>>>>>>
>>>>>>>>>>>>> than are o's avaible.
>>>>>>>>>>>> Agreed. There are aleph_0 lines, Thus there are aleph_0 o's
>>>>>>>>>>>> available.
>>>>>>>>>>> FISONs have less than aleph_0 o's.
>>>>>>>>>> Nothing you can say will change the fact that here are aleph_0
>>>>>>>>>> lines. Thus there are aleph_0 o's available.
>>>>>>>>> OK, if you believe in infinite FISONs,
>>>>>>>> Nope. I do not believe in an infinite FISON. Each line is finite.
>>>>>>> Each line is the union of all preceding lines + o.
>>>>>> Correct. Does not, nothing you say can, change the fact that there
>>>>>> are an infinite number of lines.
>>>>>
>>>>> An infinite number of finite lines. That implies that the infinity
>>>>> is potential.
>>>>
>>>> nope. there are 2 dimensions to it, one is finite, the other is
>>>> infinite.
>>>
>>> Both dimensions are infinite wrt iteration... Think of something
>>> along the lines of:
>>>
>>> [0] = 0/1, 0/2, 0/...n
>>> [1] = 1/1, 1/2, 1/...n
>>> [2] = 2/1, 2/2, 2/...n
>>> [3] = 3/1, 3/2, 3/...n
>>>
>>> [...]
>>>
>>> Humm...
>>>
>>
>> think of Cantor Pairing creating an infinite number of single numbers
>> from two numbers, and vise versa.
>>
>
> current topic is 2D to 1D mappings, but Im sure it can be extended to 3D
> to 1D mappings, (done in streaming digital TV) and why not nD to 1D ?
>
> For an n dimentional structure we have all the info on the indexes
> already, so it is a matter of serializing it.
>
> that puts Cantors Enumeration in with the baby steps.

Right. Any nD can be stored in 1D.

sergio wrote:

>>> current topic is 2D to 1D mappings, but Im sure it can be extended to
>>> 3D to 1D mappings, (done in streaming digital TV) and why not nD to 1D
>>> ?
>>> For an n dimentional structure we have all the info on the indexes
>>> already, so it is a matter of serializing it.
>>
>> MASSIVE 50 MILLION C0VID VACCINES RECALLED AS THEY TRIGGER POSITIVES IN
>> HIV TESTS
>
> population control

you mean *population_death*, not "control". Please stop talking nice
about these dirty capitalists *mass_murderers*. One death, and you had
revolutions in eastern europe. Compare that withe millions to billions in
stinking capitalism. You make me vomit, *"population_control"*. It's
death in billions, not "control". Wake the fuck up.

Chris M. Thomasson schrieb am Samstag, 12. Februar 2022 um 10:15:42 UTC+1:

> think of Cantor Pairing creating an infinite number of single numbers
> from two numbers, and vise versa.

All positive fractions m/n are contained in the matrix

1/1, 1/2, 1/3, 1/4, ...
2/1, 2/2, 2/3, 2/4, ...
3/1, 3/2, 3/3, 3/4, ...
4/1, 4/2, 4/3, 4/4, ...
5/1, 5/2, 5/3, 5/4, ...
....

Cantor claims that all can be indexed by natural numbers, i.e., written in a sequence, when he uses the sequence

1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ...

produced by his formula for the index k

k = (m + n - 1)(m + n - 2)/2 + m.

(When we enumerate the fractions in a different way like 1/1, 1/10, 1/100, ... we will obviously fail because 1/2 will never get indexed.)

Cantor's claim is tantamount to distributing all O's in

OXXX...
OXXX...
OXXX...
OXXX...
....

such that all places are covered by O's, because the first column contains just as many places as |N. At every place there sits an O. In the first step nothing would happen, because 1/1 remain where it is. After the second step the matrix would be this

OOXX...
XXXX...
OXXX...
OXXX...
....

and after the third step this

OOXX...
OXXX...
XXXX...
OXXX...
....

Now 1/1, 1/2, 2/1 are covered. And so on. After "all" there is no uncovered place X existing. Only O's.

Of course this is impossible. But if it were possible and if it were a bijection, then we could also take the reverse procedure and bring all fractions into the first column, from

1/1, 1/2, 1/3, 1/4, ...
2/1, 2/2, 2/3, 2/4, ...
3/1, 3/2, 3/3, 3/4, ...
4/1, 4/2, 4/3, 4/4, ...
5/1, 5/2, 5/3, 5/4, ...
....

to

1/1, __, __, __, ...
1/2, __, __, __, ...
2/1, __, __, __, ...
1/3, __, __, __, ...
2/2, __, __, __, ...
....

Every position in the first column is occupied at the start. The fractions residing there must not be forgotten. They must evade to another place until it's their turn to settle in the first column.

Here are the first steps eventually reaching 1/1, 1/2, 2/1, 1/3, 2/2 in the first column

1/1, 2/1, 1/3, 1/4, ... 1/1, 3/1, 1/3, 1/4, ... 1/1, 3/1, 4/1, 1/4, ... 1/1, 3/1, 4/1, 1/4, ...
1/2, 2/2, 2/3, 2/4, ... 1/2, 2/2, 2/3, 2/4, ... 1/2, 2/2, 2/3, 2/4, ... 1/2, 5/1, 2/3, 2/4, ...
3/1, 3/2, 3/3, 3/4, ... 2/1, 3/2, 3/3, 3/4, ... 2/1, 3/2, 3/3, 3/4, ... 2/1, 3/2, 3/3, 3/4, ...
4/1, 4/2, 4/3, 4/4, ... 4/1, 4/2, 4/3, 4/4, ... 1/3, 4/2, 4/3, 4/4, ... 1/3, 4/2, 4/3, 4/4, ...
5/1, 5/2, 5/3, 5/4, ... 5/1, 5/2, 5/3, 5/4, ... 5/1, 5/2, 5/3, 5/4, ... 2/2, 5/2, 5/3, 5/4, ...
.... ... ... ...

Of course this is impossible too because never a place becomes empty. And never does not mean in the infinite.

When I say shuffle, that means you can apply any other procedure you like. You will never reach the aim

1/1, __, __, __, ...
1/2, __, __, __, ...
2/1, __, __, __, ...
1/3, __, __, __, ...
2/2, __, __, __, ...
....

Countability is nonsense.

Regards, WM

On 2/13/2022 5:15 AM, WM wrote:
> Chris M. Thomasson schrieb am Samstag, 12. Februar 2022 um 10:15:42 UTC+1:
>
>> think of Cantor Pairing creating an infinite number of single numbers
>> from two numbers, and vise versa.
>
> All positive fractions m/n are contained in the matrix
>
> 1/1, 1/2, 1/3, 1/4, ...
> 2/1, 2/2, 2/3, 2/4, ...
> 3/1, 3/2, 3/3, 3/4, ...
> 4/1, 4/2, 4/3, 4/4, ...
> 5/1, 5/2, 5/3, 5/4, ...
> ...
>
> Cantor claims that all can be indexed by natural numbers, i.e., written in a sequence, when he uses the sequence
>
> 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ...
>
> produced by his formula for the index k
>
> k = (m + n - 1)(m + n - 2)/2 + m.
>

>
> Cantor's claim is tantamount to distributing all O's in
>
> OXXX...
> OXXX...
> OXXX...
> OXXX...
> ...

LIAR, that is your mess.

<snip crap>

>
> Regards, WM

On Sunday, 13 February 2022 at 10:47:26 UTC-4, sergio wrote:
> On 2/13/2022 5:15 AM, WM wrote:
> > Cantor's claim is tantamount to distributing all O's in
> >
> > OXXX...
> > OXXX...
> > OXXX...
> > OXXX...
> > ...
> LIAR, that is your mess.

He is almost right. Cantor's result states that it is possible to *replace* every 'X' with an 'O'. "Distributing" implies that there must be aleph_0 'X's still intermingled with them (which is, of course, also possible), but that is much less interesting.

sergio schrieb am Sonntag, 13. Februar 2022 um 15:47:26 UTC+1:
> On 2/13/2022 5:15 AM, WM wrote:

> > Cantor's claim is tantamount to distributing all O's in
> >
> > OXXX...
> > OXXX...
> > OXXX...
> > OXXX...
> > ...
> LIAR, that is your mess.
>
No you are simply too stupid to understand this claim of Cantor's.

Regards, WM

horand....@gmail.com schrieb am Sonntag, 13. Februar 2022 um 17:20:17 UTC+1:
> On Sunday, 13 February 2022 at 10:47:26 UTC-4, sergio wrote:
> > On 2/13/2022 5:15 AM, WM wrote:
> > > Cantor's claim is tantamount to distributing all O's in
> > >
> > > OXXX...
> > > OXXX...
> > > OXXX...
> > > OXXX...
> > > ...
> > LIAR, that is your mess.
> He is almost right.

Not almost but completely.

> Cantor's result states that it is possible to *replace* every 'X' with an 'O'. "Distributing" implies that there must be aleph_0 'X's still intermingled

No single X must remain! Because Cantor claims a single sequence like the first column.

Regards, WM

zelos...@gmail.com schrieb am Montag, 14. Februar 2022 um 06:35:11 UTC+1:
> lördag 12 februari 2022 kl. 09:55:30 UTC+1 skrev WM:

> > If the number of lines does not change, then the elements of |N cannot change and then number of O's in
> >
> > OXXX...
> > OXXX...
> > OXXX...
> > OXXX...
> > ...
> >
> > cannot change either. But Cantor claims that the O's can cover all X. Contradiction.
> > 1/1, 1/2, 1/3, 1/4, ...
> > 2/1, 2/2, 2/3, 2/4, ...
> > 3/1, 3/2, 3/3, 3/4, ...
> > 4/1, 4/2, 4/3, 4/4, ...
> > 5/1, 5/2, 5/3, 5/4, ...
> > ...
> Your argument is invalid because you assume that all injective functions must be bijective,

No, I never said so. But the argument is obvious. Cantor claims a single sequence. This is the first columns. But the other places will never get empty.

Regards, WM

On 2/14/2022 3:13 AM, WM wrote:
> sergio schrieb am Sonntag, 13. Februar 2022 um 15:47:26 UTC+1:
>> On 2/13/2022 5:15 AM, WM wrote:
>
>>> Cantor's claim is tantamount to distributing all O's in
>>>
>>> OXXX...
>>> OXXX...
>>> OXXX...
>>> OXXX...
>>> ...
>> LIAR, that is your mess.
>>
> No you are simply too stupid to understand this claim of Cantor's.
>
> Regards, WM

you used the word "tantamount" which is a vagueatuity, which I reject.

Let's see you replace "tantamount" with a direct mathematical analysis of Cantor using actual math.

Im sure you can find it somewhere and cut and paste it here.

zelos...@gmail.com schrieb am Montag, 14. Februar 2022 um 12:38:09 UTC+1:
> måndag 14 februari 2022 kl. 10:18:34 UTC+1 skrev WM:
> > > Your argument is invalid because you assume that all injective functions must be bijective,
> > No, I never said so. But the argument is obvious. Cantor claims a single sequence. This is the first columns. But the other places will never get empty.

> You stated in the other thread and we can see this is playing out in every argument you do.

I said: If there is a bijection between two sets, then every injective mapping between these two sets is a bijection.

Regards, WM

On 2/14/2022 3:18 AM, WM wrote:
> zelos...@gmail.com schrieb am Montag, 14. Februar 2022 um 06:35:11 UTC+1:
>> lördag 12 februari 2022 kl. 09:55:30 UTC+1 skrev WM:
>
>>> If the number of lines does not change, then the elements of |N cannot change and then number of O's in
>>>
>>> OXXX...
>>> OXXX...
>>> OXXX...
>>> OXXX...
>>> ...
>>>
>>> cannot change either. But Cantor claims that the O's can cover all X. Contradiction.
>>> 1/1, 1/2, 1/3, 1/4, ...
>>> 2/1, 2/2, 2/3, 2/4, ...
>>> 3/1, 3/2, 3/3, 3/4, ...
>>> 4/1, 4/2, 4/3, 4/4, ...
>>> 5/1, 5/2, 5/3, 5/4, ...
>>> ...
>> Your argument is invalid because you assume that all injective functions must be bijective,
>
> No, I never said so. But the argument is obvious. Cantor claims a single sequence. This is the first columns. But the other places will never get empty.
>
> Regards, WM
>

yours above is still nonsense dude, another failed try, and you admit that you cannot fix it.

Nothing "gets empty", they are infinite, both rows and columns.

Just use Cantors Enumeration, it is so simple and obvious and it works.

your tic-tac-toe scheme has failed totally.

On 2/14/2022 7:55 AM, WM wrote:
> zelos...@gmail.com schrieb am Montag, 14. Februar 2022 um 12:38:09 UTC+1:
>> måndag 14 februari 2022 kl. 10:18:34 UTC+1 skrev WM:
>
>>>> Your argument is invalid because you assume that all injective functions must be bijective,
>>> No, I never said so. But the argument is obvious. Cantor claims a single sequence. This is the first columns. But the other places will never get empty.
>
>> You stated in the other thread and we can see this is playing out in every argument you do.
>
> I said: If there is a bijection between two sets, then every injective mapping between these two sets is a bijection.
>
> Regards, WM
>
>

an injective mapping is not bijection.

On Monday, February 14, 2022 at 7:02:05 PM UTC+1, sergio wrote:
> On 2/14/2022 7:55 AM, WM wrote:
> > zelos...@gmail.com schrieb am Montag, 14. Februar 2022 um 12:38:09 UTC+1:
> >> måndag 14 februari 2022 kl. 10:18:34 UTC+1 skrev WM:
> >
> >>>> Your argument is invalid because you assume that all injective functions must be bijective,
> >>> No, I never said so. But the argument is obvious. Cantor claims a single sequence. This is the first columns. But the other places will never get empty.
> >
> >> You stated in the other thread and we can see this is playing out in every argument you do.
> >
> > I said: If there is a bijection between two sets, then every injective mapping between these two sets is a bijection.
> >
> > Regards, WM
> >
> >
> an injective mapping is not [necessarily a] bijection.

Clearly "between" any two sets X and Y = X there's a bijection, namely the identity function on X.

Hence there's a bijection "between" the set IN and IN, namely f: IN --> IN, f(n) = n.

But the injective function f': IN --> IN, f'(n) = n+1 is not a bijection from IN onto IN.

Hence WM's claim is wrong (in the context of "transfinite set theory"). Actually, in the context of ZFC it is equivalent with the claim: "All sets are finite."

On 2/13/2022 3:15 AM, WM wrote:
> Chris M. Thomasson schrieb am Samstag, 12. Februar 2022 um 10:15:42 UTC+1:
>
>> think of Cantor Pairing creating an infinite number of single numbers
>> from two numbers, and vise versa.
>
> All positive fractions m/n are contained in the matrix
>
> 1/1, 1/2, 1/3, 1/4, ...
> 2/1, 2/2, 2/3, 2/4, ...
> 3/1, 3/2, 3/3, 3/4, ...
> 4/1, 4/2, 4/3, 4/4, ...
> 5/1, 5/2, 5/3, 5/4, ...
> ...
>
> Cantor claims that all can be indexed by natural numbers, i.e., written in a sequence, when he uses the sequence
[...]

The set of natural numbers is infinite. Therefore, it can be used to
index any other infinite set. Period. Keep in mind that any n-dimension
set can be stored and indexed in a 1-d set, and vise versa.

On 2/14/2022 1:18 AM, WM wrote:
> zelos...@gmail.com schrieb am Montag, 14. Februar 2022 um 06:35:11 UTC+1:
>> lördag 12 februari 2022 kl. 09:55:30 UTC+1 skrev WM:
>
>>> If the number of lines does not change, then the elements of |N cannot change and then number of O's in
>>>
>>> OXXX...
>>> OXXX...
>>> OXXX...
>>> OXXX...
>>> ...
>>>
>>> cannot change either. But Cantor claims that the O's can cover all X. Contradiction.
>>> 1/1, 1/2, 1/3, 1/4, ...
>>> 2/1, 2/2, 2/3, 2/4, ...
>>> 3/1, 3/2, 3/3, 3/4, ...
>>> 4/1, 4/2, 4/3, 4/4, ...
>>> 5/1, 5/2, 5/3, 5/4, ...
>>> ...
>> Your argument is invalid because you assume that all injective functions must be bijective,
>
> No, I never said so. But the argument is obvious. Cantor claims a single sequence. This is the first columns. But the other places will never get empty.

I don't think that you understand that any 2-ary infinite tree can be
stored in a 1-ary infinite tree.

"Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:

> I don't think that you understand that any 2-ary infinite tree can be
> stored in a 1-ary infinite tree.

Well I, for one, don't! What does "can be stored in" mean?

--
Ben.

On 2/14/2022 4:17 PM, Ben Bacarisse wrote:
> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>
>> I don't think that you understand that any 2-ary infinite tree can be
>> stored in a 1-ary infinite tree.
>
> Well I, for one, don't! What does "can be stored in" mean?
>

Think of storing a 2-ary balanced infinite tree in a 1-ary infinite
array. It can be done. Storing a 3d tree in a 1d array is possible as
well. Think of index, offset type of methods to find the nodes, parent
children, say a 2-ary tree in a 1-ary array...

"Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:

> On 2/14/2022 4:17 PM, Ben Bacarisse wrote:
>> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>>
>>> I don't think that you understand that any 2-ary infinite tree can be
>>> stored in a 1-ary infinite tree.
>> Well I, for one, don't! What does "can be stored in" mean?
>>
>
> Think of storing a 2-ary balanced infinite tree in a 1-ary infinite
> array.

Adding another undefined concept is not the best way to define something
else. I now don't know what two kinds of "storing" are rather than just
one.

> It can be done.

So you say, but since I don't know what "it" is, I asked for an
explanation.

> Storing a 3d tree in a 1d array is possible as
> well.

I think some words may have got mixed up. 3d tree?

> Think of index, offset type of methods to find the nodes, parent
> children, say a 2-ary tree in a 1-ary array...

Do you just mean that there is a one-to-one mapping between the nodes?
That's not a very interesting claim, but I would not call that "storing"
one tree "in" another. A tree has edges and therefore paths. The
complete infinite binary tree has more paths then the complete infinite
unary tree, so the word "storing" must be covering something up.

Maybe something more concrete wold help. If the set of nodes (for both
trees) is N (the natural numbers), the binary tree has edge set {(n,
2n), (n, 2n+1)} and the unary tree has edge set {(n, n+1)} (with n in N
in both cases). What does it mean to store the first in the second?

--
Ben.

On 2/14/2022 7:14 PM, Ben Bacarisse wrote:
> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>
>> On 2/14/2022 4:17 PM, Ben Bacarisse wrote:
>>> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>>>
>>>> I don't think that you understand that any 2-ary infinite tree can be
>>>> stored in a 1-ary infinite tree.
>>> Well I, for one, don't! What does "can be stored in" mean?
>>>
>>
>> Think of storing a 2-ary balanced infinite tree in a 1-ary infinite
>> array.
>
> Adding another undefined concept is not the best way to define something
> else. I now don't know what two kinds of "storing" are rather than just
> one.
>
>> It can be done.
>
> So you say, but since I don't know what "it" is, I asked for an
> explanation.
[...]
> Maybe something more concrete wold help. If the set of nodes (for both
> trees) is N (the natural numbers), the binary tree has edge set {(n,
> 2n), (n, 2n+1)} and the unary tree has edge set {(n, n+1)} (with n in N
> in both cases). What does it mean to store the first in the second?
>

Read all:

https://groups.google.com/g/sci.math/c/x2lN4l9gdRo/m/0eIvXY8QAwAJ

On 2/14/2022 7:14 PM, Ben Bacarisse wrote:
> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
[...]
> in both cases). What does it mean to store the first in the second?

From one node we can find its parent nodes. Also, we can find its child
nodes. n-ary.

On 2/14/2022 7:14 PM, Ben Bacarisse wrote:
> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>
>> On 2/14/2022 4:17 PM, Ben Bacarisse wrote:
>>> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
[...]
> Maybe something more concrete wold help. If the set of nodes (for both
> trees) is N (the natural numbers), the binary tree has edge set {(n,
> 2n), (n, 2n+1)} and the unary tree has edge set {(n, n+1)} (with n in N
> in both cases). What does it mean to store the first in the second?
>

Think of being able to store/load data in the n-ary roots of a complex
number...

http://fractallife247.com/test/rifc_cipher/