On 5/6/2022 3:04 PM, WM wrote:
> William schrieb am Freitag, 6. Mai 2022 um 17:53:15 UTC+2:
>> On Friday, May 6, 2022 at 9:34:48 AM UTC-3, WM wrote:
>>> William schrieb am Donnerstag, 5. Mai 2022 um 22:13:10 UTC+2:
>>>
>>>> Nope. Cardinality is an equivalence class of sets is not a metric. "ω - n = ω" is shorthand for the set ({1,2,3,...} \ {1,2,3...,n}) has cardinality aleph_0.
>>> And that is shorthand for: the set of natural numbers which can be inserted at position n is finite
>> Nope, "the set of natural numbers which can be inserted at position n", is word salad.
>
> That means you are unable to comprehend it. It does not mean that everybody is unable.

no, it means you are unclear. So how do you stick ℕ into n ? Just write it out using Math and equations.

be careful though, you have made too many mistakes today, it is because you answer too quickly without thinking.

>
>> We have
>>
>> for n element of N_p, |{1,2,3,...} \ {1,2,3...,n}| = infinity
>>
>> Note that N_p= {1,2,3,...} is a Peano set and does not contain "dark" elements.
>
> Note that this opinion is wrong because it contradicts simplest logic.

Wrong, you cannot brush away facts, nor proofs.

>
> Since all n have infinite distance from omega, there is no n closer to omega. But something is closer, unless there is an infinite gap.

Try n+1, it is closer than n to omega.

>
> Regards, WM
>

lad, you have a long way to go

On 5/6/2022 3:12 PM, WM wrote:
> Jim Burns schrieb am Freitag, 6. Mai 2022 um 16:53:41 UTC+2:
>> On 5/6/2022 9:55 AM, WM wrote:
>>> Jim Burns schrieb
>>> am Freitag, 6. Mai 2022 um 15:14:56 UTC+2:
>>>> Ordinals are the things for which
>>>> each non-empty collection contains a first.
>>>
>>> Wrong for dark ordinals.
>> Ordinals are defined to be the things for which
>> each non-empty collection contains a first.
>> Compare to
>> Right triangles are plane figures with
>> three corners, one of which is a right angle.
>>
>> If Pythagoras makes a claim about _each right triangle_
>> it is not refuted by pointing to an equilateral
>> triangle.
>
> But if he makes his claim for all triangles

Pythagoras did not. did you read the above post at all ? You missed the point of it.

>>
> Regards, WM

On 5/6/2022 5:45 PM, sergio wrote:
> On 5/6/2022 2:09 PM, Chris M. Thomasson wrote:
>> On 5/6/2022 11:18 AM, sergio wrote:
>>> On 5/6/2022 9:50 AM, WM wrote:
>>>> sergio schrieb am Freitag, 6. Mai 2022 um 16:33:05 UTC+2:
>>>>> On 5/6/2022 8:45 AM, WM wrote:
>>>>
>>>>>> No, that IS the distance.
>>>>>>
>>>>> No, distance has units.
>>>>>
>>>> Yes, in natnumbers the unit is 1, the unit.
>>>>
>>>> Regards, WM
>>>
>>>
>>>
>>>      1 is a value, not a unit.
>>
>> I define the radius of the unit circle as, one.
>
> 1 = i^4
>
>    also, 1 = i^(4*n) for all n, including those just aft of omega
> (note: aft => relative vector direction but no value, no units)
>
>
>  does 1 kill the imagination ?  or is it even numbers ?

1 Unit can be, say, one inch. Or, perhaps 4 inches? Or 7/8'ths.
Whatever. The fact is that the unit circle in my personal programming
realm has a radius of 1 unit. A unit is abstract and can be defined to a
great many things... ;^)

On 5/6/2022 5:45 PM, sergio wrote:
> On 5/6/2022 2:09 PM, Chris M. Thomasson wrote:
>> On 5/6/2022 11:18 AM, sergio wrote:
>>> On 5/6/2022 9:50 AM, WM wrote:
>>>> sergio schrieb am Freitag, 6. Mai 2022 um 16:33:05 UTC+2:
>>>>> On 5/6/2022 8:45 AM, WM wrote:
>>>>
>>>>>> No, that IS the distance.
>>>>>>
>>>>> No, distance has units.
>>>>>
>>>> Yes, in natnumbers the unit is 1, the unit.
>>>>
>>>> Regards, WM
>>>
>>>
>>>
>>>      1 is a value, not a unit.
>>
>> I define the radius of the unit circle as, one.
>
> 1 = i^4
>
>    also, 1 = i^(4*n) for all n, including those just aft of omega
> (note: aft => relative vector direction but no value, no units)
>
>
>  does 1 kill the imagination ?  or is it even numbers ?

The unit circle is in red here:

http://fractallife247.com/test/

My code is there for all to see. Try clicking around to plot a field
line per click... ;^)

On 5/2/2022 7:40 PM, Chris M. Thomasson wrote:
> On 5/2/2022 4:43 PM, Fritz Feldhase wrote:
>> On Tuesday, May 3, 2022 at 12:14:56 AM UTC+2, Chris M. Thomasson wrote:
>>> On 5/1/2022 8:43 AM, William wrote:
>>>>
>>>> Let natural numbers.|N be {N_p N_d} with N_p a Peano set and N_p a
>>>> set of "dark" elements. Start off with no elements in vase 1 and
>>>> each element of |N in vase 2. At step n, we mover element n, from
>>>> N_p in vase 2 to vase 1. There is a set n iff n is in N_p.. At every
>>>> step n, vase 1 contains a finite set of elements and vase 2 contains
>>>> an infinite subset of N_p and N_d. We do not need N_d to insure that
>>>> vase 2 contains and infinite number of elements
>>>> Note we never touch N_d so each element of N_d remains in vase 2.
>>>>
>>>> We now continue until each element of N_p is in vase 1, (This takes
>>>> an infinite number of steps.)
>>>>
>>>> At this point
>>> Humm... If it takes an infinite number of steps to fill vase 1, then at
>>> what point can you say its full?
>>
>> I guess, he's considering a "super task". We start at t = 0. At t = 1
>> - 1/2 the first number, 1, is moved to vase 1. At t = 1 - 1/3 the
>> second number, 2, is moved, at t = 1 - 1/4 the third number, 3, is
>> moved and so on. Actually, it's easy to show that (in this case) for
>> each and every number n there's a certain time t < 1, namely 1 - 1/(n
>> + 1) , where n is moved to vase 1. Hence at t = 1 each and every
>> number (in N_p) has been moved to vase 1.
>>
>> So I'd say at t = 1 it's reasonable to claim that /now/ vase 1 is
>> filled with all elements in N_p.
>>
>> Yes, the process of "moving the numbers" does not have a last step. On
>> the other hand, which number has n o t been moved to vase 1 at t = 1? :-P
>>
>> For each and every t < 1 there are still infinitely many numbers which
>> have to be moved to vase 1, but at t = 1 the job has been done. Such
>> is the power of an "unlimited" speed up of a process.
>
> I see. It seems to be akin to me writing the word "pi". I mean pi in
> _all_ of it's infinite glory; t = 1, 100% complete. Not, t = .001, or t
> = .5... I mean pi as in t = 1. ;^)
>
> pi means pi with infinite precision in a sense. Does that sound kosher
> at all?
>
> I suppose I can write something like pi(5) which means 5 digits of pi
> where pi(5) = 3.1415, and p(1) = 3, ect.. ;^)

Actually, using the notation above:

pi(infinity) = pi

Humm... Sound alright?

Chris M. Thomasson wrote:

>> I suppose I can write something like pi(5) which means 5 digits of pi
>> where pi(5) = 3.1415, and p(1) = 3, ect.. ;^)
>
> Actually, using the notation above: pi(infinity) = pi Humm... Sound
> alright?

yes, it seems to be alright. But you slavic nazis don't want people
believe what you nazis do along your systems. What is your name, Christov
M. Thomaselenski??

Croatian fighter captured in Ukraine speaks to RT
https://www.bitchute.com/video/mNUCQg0O7Mf0/

ohh my, a nazi, among the nazis, from "ukraine", the poorest shithole in
europe, since 1989 till today, NOT a member of nazi_nato, NOT a member of
EU etc, is calling the strongest and biggest economy in europe, the
fathers of Mercedes and BMW, for being *_a_sulky_liver_sausage_*. Ohh my
ass, this world turns shit upside-down.

On 5/6/2022 4:12 PM, WM wrote:
> Jim Burns schrieb
> am Freitag, 6. Mai 2022 um 16:53:41 UTC+2:
>> On 5/6/2022 9:55 AM, WM wrote:
>>> Jim Burns schrieb
>>> am Freitag, 6. Mai 2022 um 15:14:56 UTC+2:

>>>> Ordinals are the things for which
>>>> each non-empty collection contains a first.
>>>
>>> Wrong for dark ordinals.
>>
>> Ordinals are defined to be the things for which
>> each non-empty collection contains a first.
>> Compare to
>> Right triangles are plane figures with
>> three corners, one of which is a right angle.
>>
>> If Pythagoras makes a claim about _each right triangle_
>> it is not refuted by pointing to an equilateral
>> triangle.
>
> But if he makes his claim for all triangles because
> he thinks that all triangles are right triangles,
> then he must be corrected.

Pythagoras is not making just any old claim.
He is making a claim with an argument in support.
The argument uses what we already know about...
....about what? Triangles? Right triangles?