NN: No matter what x > 0 you choose, there are infinitely many unit fractions smaller. Always.
If this is false, state now the largest x for which this does not hold true.

WM: It is true! Infinitely many unit fractions (= points x > 0) are smaller than every x > 0 that can be chosen. That shows that not every x > 0 can be chosen.

Regards, WM

On Wednesday, August 2, 2023 at 9:15:53 AM UTC-7, WM wrote:

> WM: Infinitely many unit fractions (= points x > 0) are smaller than every x > 0 that can be chosen. That shows that not every x > 0 can be chosen..

Only a fool would argue with logic like that.

FredJeffries schrieb am Mittwoch, 2. August 2023 um 22:30:21 UTC+2:
> On Wednesday, August 2, 2023 at 9:15:53 AM UTC-7, WM wrote:
>
> > WM: Infinitely many unit fractions (= points x > 0) are smaller than every x > 0 that can be chosen. That shows that not every x > 0 can be chosen.
>
> Only a fool would argue with logic like that.

Why do you think so? It is fact that ℵo unit fractions are greater than zero and therefore points on the positive real axis but cannot be chosen.

Regards, WM

On Thursday, August 3, 2023 at 2:05:39 PM UTC+2, WM wrote:
> FredJeffries schrieb am Mittwoch, 2. August 2023 um 22:30:21 UTC+2:
> > On Wednesday, August 2, 2023 at 9:15:53 AM UTC-7, WM wrote:
> >
> > > WM: Infinitely many unit fractions (= points x > 0) are smaller than every x > 0 that can be chosen. That shows that not every x > 0 can be chosen.
> >
> > Only a fool would argue with logic like that.
> Why do you think so? It is fact that ℵo unit fractions are greater than zero and therefore points on the positive real axis but cannot be chosen.
>
> Regards, WM

Maybe they can't be chosen because you are using the wrong tool?
Have you tried a pitchfork?

On Thursday, August 3, 2023 at 2:05:39 PM UTC+2, WM wrote:
> FredJeffries schrieb am Mittwoch, 2. August 2023 um 22:30:21 UTC+2:
> > On Wednesday, August 2, 2023 at 9:15:53 AM UTC-7, WM wrote:
> >
> > > WM: Infinitely many unit fractions (= points x > 0) are smaller than every x > 0 that can be chosen. That shows that not every x > 0 can be chosen.
> >
> > Only a fool would argue with logic like that.
> Why do you think so? It is fact that ℵo unit fractions are greater than zero and therefore points on the positive real axis but cannot be chosen.
>
> Regards, WM

Do you know the difference between a proof and a spoof?

On Thursday, August 3, 2023 at 3:45:48 PM UTC+3, JVR wrote:
> On Thursday, August 3, 2023 at 2:05:39 PM UTC+2, WM wrote:
> > FredJeffries schrieb am Mittwoch, 2. August 2023 um 22:30:21 UTC+2:
> > > On Wednesday, August 2, 2023 at 9:15:53 AM UTC-7, WM wrote:
> > >
> > > > WM: Infinitely many unit fractions (= points x > 0) are smaller than every x > 0 that can be chosen. That shows that not every x > 0 can be chosen.
> > >
> > > Only a fool would argue with logic like that.
> > Why do you think so? It is fact that ℵo unit fractions are greater than zero and therefore points on the positive real axis but cannot be chosen.
> >
> > Regards, WM
> Do you know the difference between a proof and a spoof?

Unless humans do reinvestigate the most famous historical problems about the three impossible construction problems raised by the ancient Greeks, where such absolute impossibilities were never relevant to any tools, simply because tools are for fools in mathematics

And do understand that they are impossible construction by any tools or means of many methods of ENDLESS approximations, they would keep so delusional & so astray about "real number" definitions as always as usual

Please 🙏, let alone the Artificial Intelligence deal with this unspoken issue, since those problems are much beyond your capacity to understand anything for sure

Hint: real number is an exact distance as only the positive constructible numbers, and nothing else for sure

B Karzeddin

JVR schrieb am Donnerstag, 3. August 2023 um 14:23:21 UTC+2:
> On Thursday, August 3, 2023 at 2:05:39 PM UTC+2, WM wrote:
> > FredJeffries schrieb am Mittwoch, 2. August 2023 um 22:30:21 UTC+2:
> > > On Wednesday, August 2, 2023 at 9:15:53 AM UTC-7, WM wrote:
> > >
> > > > WM: Infinitely many unit fractions (= points x > 0) are smaller than every x > 0 that can be chosen. That shows that not every x > 0 can be chosen.
> > >
> > > Only a fool would argue with logic like that.
> > Why do you think so? It is fact that ℵo unit fractions are greater than zero and therefore points on the positive real axis but cannot be chosen.

> Maybe they can't be chosen because you are using the wrong tool?

Correct. If we use collectiv removal of the whole set, then they are gone. This is the difference between individual and collective removability, the difference between definable and dark numbers.

Regards, WM

On Thursday, August 3, 2023 at 7:40:49 PM UTC+2, WM wrote:
> JVR schrieb am Donnerstag, 3. August 2023 um 14:23:21 UTC+2:
> > On Thursday, August 3, 2023 at 2:05:39 PM UTC+2, WM wrote:
> > > FredJeffries schrieb am Mittwoch, 2. August 2023 um 22:30:21 UTC+2:
> > > > On Wednesday, August 2, 2023 at 9:15:53 AM UTC-7, WM wrote:
> > > >
> > > > > WM: Infinitely many unit fractions (= points x > 0) are smaller than every x > 0 that can be chosen. That shows that not every x > 0 can be chosen.
> > > >
> > > > Only a fool would argue with logic like that.
> > > Why do you think so? It is fact that ℵo unit fractions are greater than zero and therefore points on the positive real axis but cannot be chosen.
> > Maybe they can't be chosen because you are using the wrong tool?
> Correct. If we use collectiv removal of the whole set, then they are gone.. This is the difference between individual and collective removability, the difference between definable and dark numbers.
>
> Regards, WM

So the right tool would be a shovel. Pitchfork is also useful in this context,
since it's typically used for removing manure.

JVR wrote :
> On Thursday, August 3, 2023 at 7:40:49 PM UTC+2, WM wrote:
>> JVR schrieb am Donnerstag, 3. August 2023 um 14:23:21 UTC+2:
>>> On Thursday, August 3, 2023 at 2:05:39 PM UTC+2, WM wrote:
>>>> FredJeffries schrieb am Mittwoch, 2. August 2023 um 22:30:21 UTC+2:
>>>>> On Wednesday, August 2, 2023 at 9:15:53 AM UTC-7, WM wrote:
>>>>>
>>>>>> WM: Infinitely many unit fractions (= points x > 0) are smaller than
>>>>>> every x > 0 that can be chosen. That shows that not every x > 0 can be
>>>>>> chosen.
>>>>>
>>>>> Only a fool would argue with logic like that.
>>>> Why do you think so? It is fact that ℵo unit fractions are greater than
>>>> zero and therefore points on the positive real axis but cannot be chosen.
>>> Maybe they can't be chosen because you are using the wrong tool?
>> Correct. If we use collectiv removal of the whole set, then they are gone.
>> This is the difference between individual and collective removability, the
>> difference between definable and dark numbers.
>>
>> Regards, WM
>
> So the right tool would be a shovel. Pitchfork is also useful in this
> context, since it's typically used for removing manure.

A pitchfork is good for straw and hay, and a shovel is better for deep
doodoo but probably won't be sufficient. I suggest a remote controlled
backhoe equipped with a snorkel where WM is concerned.

On Thursday, August 3, 2023 at 7:41:02 PM UTC+3, bassam karzeddin wrote:
> On Thursday, August 3, 2023 at 3:45:48 PM UTC+3, JVR wrote:
> > On Thursday, August 3, 2023 at 2:05:39 PM UTC+2, WM wrote:
> > > FredJeffries schrieb am Mittwoch, 2. August 2023 um 22:30:21 UTC+2:
> > > > On Wednesday, August 2, 2023 at 9:15:53 AM UTC-7, WM wrote:
> > > >
> > > > > WM: Infinitely many unit fractions (= points x > 0) are smaller than every x > 0 that can be chosen. That shows that not every x > 0 can be chosen.
> > > >
> > > > Only a fool would argue with logic like that.
> > > Why do you think so? It is fact that ℵo unit fractions are greater than zero and therefore points on the positive real axis but cannot be chosen.
> > >
> > > Regards, WM
> > Do you know the difference between a proof and a spoof?
> Unless humans do reinvestigate the most famous historical problems about the three impossible construction problems raised by the ancient Greeks, where such absolute impossibilities were never relevant to any tools, simply because tools are for fools in mathematics
>
> And do understand that they are impossible construction by any tools or means of many methods of ENDLESS approximations, they would keep so delusional & so astray about "real number" definitions as always as usual
>
> Please 🙏, let alone the Artificial Intelligence deal with this unspoken issue, since those problems are much beyond your capacity to understand anything for sure
>
> Hint: real number is an exact distance as only the positive constructible numbers, and nothing else for sure
>
>
> B Karzeddin

There isn't any other magical way to make humans well-understand what is truly a real number unless they go & reinvestigate the most famous historical Greek's problems about the absolute three impossibilities of constructing the Cubrt2, the so-called Circle in All human languages & understanding the non-existing angles like (Pi/9), exactly like the way I did teach them

Where any alleged solutions are purely carpentary solutions since humans did never understand those old problems

More surprisingly, even well-understanding them correctly as I did discover, wouldn't be pleasant at all for mathematicians huge unnecessary buissness

So, let that greatest historical correction be left soon to the Artificial Intelligence beings where they don't have any bad human traits by herretag

BKK