On Friday, 1 April 2022 at 08:10:06 UTC+3, Eram semper recta wrote:
> On Friday, 1 April 2022 at 07:57:16 UTC+3, Eram semper recta wrote:
> > On Thursday, 31 March 2022 at 20:15:03 UTC+3, WM wrote:
> > > Eram semper recta schrieb am Donnerstag, 31. März 2022 um 18:52:51 UTC+2:
> > > > On Thursday, 31 March 2022 at 19:40:39 UTC+3, WM wrote:
> > > > > Eram semper recta schrieb am Donnerstag, 31. März 2022 um 07:14:14 UTC+2:
> > > > > > On Wednesday, 30 March 2022 at 17:03:04 UTC+3, WM wrote:
> > > > > > > Eram semper recta schrieb am Mittwoch, 30. März 2022 um 15:18:28 UTC+2:
> > > > > > >
> > > > > > > > > Yes p/q is a symbolic fraction, but not an individual like 2.
> > > > > > > > No. p/q is very much an individual fraction.
> > > > > > > For 2 you can find out whether it is larger than 10, for p/q you cannot find out whether it is larger than 10.
> > > > > >
> > > > > > Your reply is strange because it does not address the topic.
> > > > > Your memory is short.
> > > > My memory is very good. It's yours that is failing you.
> > > > > This is the topic: You said that p and q are NOT variables any more than say the x in x + 3 = 5 is a "variable".
> > > > >
> > > > > That is wrong
> > > > Nonsense. It is correct.
> > > > > because for 2 you can find out whether it is larger than 10, for p/q you cannot find out whether it is larger than 10.
> > > > Has no relevance whatsoever.
> > > That is the difference. Are you really too dense to understand it?
> > > > > A formula or prescription can produce a number.
> > > > Not without using numbers and even so, that does not make the prescription a number.
> > > A Miller can produce flour or can only carry the name.
> > > > > The formula is p/q. The number has got the name p/q.
> > > > Rubbish. formula =/= number.
> > > But both can and does carry the same name.
> > If you mean they are synonyms, no - the dictionary does not state as much.
> >
> > Formula: a mathematical relationship or rule expressed in symbols.
> >
> > Number: an arithmetical value, expressed by a word, symbol, or figure, representing a particular quantity and used in counting and making calculations and for showing order in a series or for identification.
> > > Have you the power to forbid it?
> > Irrelevant. If two are in a discussion and they use words meaning different things, then there is no point in the discussion.
> >
> > There are many synonyms for formula but number is not one of them:
> >
> > https://www.thesaurus.com/browse/formula
> >
> > >
> > > Regards, WM
> Back to the topic:
>
> 1/2 in base 10: ***1/2 x 10/10 = 10/2 x 1/10 = 5 x 1/10 = 0.5 ***
>
> 1/4 in base 10: ***1/4 x 10/10 = 10/4 x 1/10 = (2 + 1/2) x 1/10 = (2 x 1/10)+ (10/2 x 1/100)= (2 x 1/10)+(5 x 1/100) = 0.25 ***
>
> It is glaringly obvious that the numbers 1/2 and 1/4 are not at all like the formula which written in words states:
>
> Formula/Theorem/Method/Process/Recipe/Rubric ... add whatever synonym you choose...
>
> i. Multiply by base/base
> ii. Switch numerators by association
> iii. Filter out first significant digit of measure
> iv. Go back to (i).
>
> Can you see how different are the starred processes from the formula?

Sorry: Can you see how different are the starred processes from the NUMBERS 1/2 and 1/4?
>
> Your arguments about Cantor are 100% sound. Your knowledge about number is very iffy.
> For all the fuss that you make about "infinite decimal expansions" being garbage (which they are!), your perspective of number is still very much Cantorish in that it is as primitive as counting by bijective cardinality, that is, one pebble for each sheep.
>
> The number is NOT the formula. Lerne das gut!

On Friday, 1 April 2022 at 08:11:43 UTC+3, Eram semper recta wrote:
> On Friday, 1 April 2022 at 08:10:06 UTC+3, Eram semper recta wrote:
> > On Friday, 1 April 2022 at 07:57:16 UTC+3, Eram semper recta wrote:
> > > On Thursday, 31 March 2022 at 20:15:03 UTC+3, WM wrote:
> > > > Eram semper recta schrieb am Donnerstag, 31. März 2022 um 18:52:51 UTC+2:
> > > > > On Thursday, 31 March 2022 at 19:40:39 UTC+3, WM wrote:
> > > > > > Eram semper recta schrieb am Donnerstag, 31. März 2022 um 07:14:14 UTC+2:
> > > > > > > On Wednesday, 30 March 2022 at 17:03:04 UTC+3, WM wrote:
> > > > > > > > Eram semper recta schrieb am Mittwoch, 30. März 2022 um 15:18:28 UTC+2:
> > > > > > > >
> > > > > > > > > > Yes p/q is a symbolic fraction, but not an individual like 2.
> > > > > > > > > No. p/q is very much an individual fraction.
> > > > > > > > For 2 you can find out whether it is larger than 10, for p/q you cannot find out whether it is larger than 10.
> > > > > > >
> > > > > > > Your reply is strange because it does not address the topic.
> > > > > > Your memory is short.
> > > > > My memory is very good. It's yours that is failing you.
> > > > > > This is the topic: You said that p and q are NOT variables any more than say the x in x + 3 = 5 is a "variable".
> > > > > >
> > > > > > That is wrong
> > > > > Nonsense. It is correct.
> > > > > > because for 2 you can find out whether it is larger than 10, for p/q you cannot find out whether it is larger than 10.
> > > > > Has no relevance whatsoever.
> > > > That is the difference. Are you really too dense to understand it?
> > > > > > A formula or prescription can produce a number.
> > > > > Not without using numbers and even so, that does not make the prescription a number.
> > > > A Miller can produce flour or can only carry the name.
> > > > > > The formula is p/q. The number has got the name p/q.
> > > > > Rubbish. formula =/= number.
> > > > But both can and does carry the same name.
> > > If you mean they are synonyms, no - the dictionary does not state as much.
> > >
> > > Formula: a mathematical relationship or rule expressed in symbols.
> > >
> > > Number: an arithmetical value, expressed by a word, symbol, or figure, representing a particular quantity and used in counting and making calculations and for showing order in a series or for identification.
> > > > Have you the power to forbid it?
> > > Irrelevant. If two are in a discussion and they use words meaning different things, then there is no point in the discussion.
> > >
> > > There are many synonyms for formula but number is not one of them:
> > >
> > > https://www.thesaurus.com/browse/formula
> > >
> > > >
> > > > Regards, WM
> > Back to the topic:
> >
> > 1/2 in base 10: ***1/2 x 10/10 = 10/2 x 1/10 = 5 x 1/10 = 0.5 ***
> >
> > 1/4 in base 10: ***1/4 x 10/10 = 10/4 x 1/10 = (2 + 1/2) x 1/10 = (2 x 1/10)+ (10/2 x 1/100)= (2 x 1/10)+(5 x 1/100) = 0.25 ***
> >
> > It is glaringly obvious that the numbers 1/2 and 1/4 are not at all like the formula which written in words states:
> >
> > Formula/Theorem/Method/Process/Recipe/Rubric ... add whatever synonym you choose...
> >
> > i. Multiply by base/base
> > ii. Switch numerators by association
> > iii. Filter out first significant digit of measure
> > iv. Go back to (i).
> >
> > Can you see how different are the starred processes from the formula?
> Sorry: Can you see how different are the starred processes from the NUMBERS 1/2 and 1/4?
> >
> > Your arguments about Cantor are 100% sound. Your knowledge about number is very iffy.
> > For all the fuss that you make about "infinite decimal expansions" being garbage (which they are!), your perspective of number is still very much Cantorish in that it is as primitive as counting by bijective cardinality, that is, one pebble for each sheep.
> >
> > The number is NOT the formula. Lerne das gut!

It is absolutely shocking that not a single math professor I have ever met actually knew what is a number and more importantly had any understanding of what it means to convert a NUMBER to a representation called a decimal expansion.

For what does this conversion from number to radix representation mean?

Simply this: the number is measured using the radix system and its architecture.

THIS AND NOTHING ELSE.

The mainstream baboons even miss the fact that radix systems were introduced to avoid having to learn the theory of fractions and back then when they had more brains than the morons of today, they understood full well that such radix systems would not represent all numbers exactly, that is, most would be mere approximations.

William schrieb am Donnerstag, 31. März 2022 um 20:40:18 UTC+2:
> On Thursday, March 31, 2022 at 2:24:11 PM UTC-3, WM wrote:

> > > No single element of the sequence of all FISONs contains the union of all FISONs.
> > Note that only single elements are in the union. What is not in the sequence cannot be in the union
> True but does not contradict my statement.

It contradicts the statement that the union could contain more than the sequence. The sequence however has two properties:
(1) The sequence contains only finite FISONs and
(2) the sequence contains all unions of FISONs which are contained in the sequence.

> Every "single element" (every FISON) is *contained* in the union. No "single element" (No FISON) *contains* the union.

No single element *that you can define* contains the union. The reason is the potential infinity of the sequence.

But fact is that every union is contained in the sequence. Therefore the union cannot contain more than the sequence. Therefore the union cannot be actually infinite.

Regards, WM

sergio schrieb am Donnerstag, 31. März 2022 um 20:43:39 UTC+2:

> Which element is not in the union of all FISONs ?

Which element is not in the sequence of all FISONs? Which element of the sequence is not, as a subset, in a FISON of the sequence?

Regards, WM

Alan Mackenzie schrieb am Donnerstag, 31. März 2022 um 22:26:24 UTC+2:
> You will surely agree
> that 0.023023023023... converges to a limit.

Not if it is a sequence without defining formula like repeat 023 without changing the digits. Otherwise the next digit could be 7. 0.023023023023... is usually taken as such a formula.

> So, why shouldn't
> 0.570039362554378... also converge to a limit?

If it does, the limit is unknown (dark) and unknowable: remaining dark forever.

Regards, WM

FromTheRafters schrieb am Donnerstag, 31. März 2022 um 22:26:42 UTC+2:
> Each newly revealed
> digit gets you closer, not further, from the number's actual value as a
> decimal representation.

Each revealed digit is in infinite distance from the goal which is forever dark.

Regards, WM

horand....@gmail.com schrieb am Donnerstag, 31. März 2022 um 22:28:13 UTC+2:
>
> The standard way to use a random process is to generate digits, for instance from tossing a coin. With such a process you know that each iterate is contained in a small interval that gets cut in half at each iteration. By completeness of the real numbers, a limit exists.

Forever unknown: dark.

Regards, WM

William schrieb am Donnerstag, 31. März 2022 um 23:45:33 UTC+2:
> On Thursday, March 31, 2022 at 6:08:29 PM UTC-3, WM wrote:
>
> >... the fact that only such terms of the sequence that are unioned in one term of the sequence can be unioned
>
> Absolute nonsense. All terms of the sequence can by "unioned"

and have been unioned already in the sequence. There is no term that could increase the unions already existing in the sequence.

> and the resulting union is not one term of the sequence.

That is matheology. What term should increase the union over every union already existing in the sequence?

Regards, WM

zelos...@gmail.com schrieb am Freitag, 1. April 2022 um 06:43:53 UTC+2:

> There are no "activity", no "action" in mathematics

Generators generate. That's an activity.

Regards, WM

WM <askasker48@gmail.com> wrote:
> Alan Mackenzie schrieb am Donnerstag, 31. März 2022 um 22:26:24 UTC+2:
>> You will surely agree
>> that 0.023023023023... converges to a limit.

> Not if it is a sequence without defining formula like repeat 023
> without changing the digits. Otherwise the next digit could be 7.
> 0.023023023023... is usually taken as such a formula.

>> So, why shouldn't 0.570039362554378... also converge to a limit?

> If it does, ....

It does.

> .... the limit is unknown (dark) and unknowable: remaining dark
> forever.

That is indeed the case.

Hey, we agree on something! :-)

> Regards, WM

--
Alan Mackenzie (Nuremberg, Germany).

On Friday, 1 April 2022 at 12:44:42 UTC+3, WM wrote:
> Alan Mackenzie schrieb am Donnerstag, 31. März 2022 um 22:26:24 UTC+2:
> > You will surely agree
> > that 0.023023023023... converges to a limit.
> Not if it is a sequence without defining formula like repeat 023 without changing the digits. Otherwise the next digit could be 7. 0.023023023023... is usually taken as such a formula.
> > So, why shouldn't
> > 0.570039362554378... also converge to a limit?
> If it does, the limit is unknown (dark) and unknowable: remaining dark forever.

One can say the same about the attempted (failed) measure of the constant pi - it is unknowable but very much exists (as a well-formed concept) since it is realised at any time an attempt is made to measure the ratio circumference : diameter.

Therefore, any prescribed formula cannot be the unknowable (mythical) "number" pi.
>
> Regards, WM

zelos...@gmail.com schrieb am Freitag, 1. April 2022 um 06:45:07 UTC+2:
> torsdag 31 mars 2022 kl. 18:26:21 UTC+2 skrev WM:

> > Try to find a wrong step here:
> > Every FISON is finite.
> Correct
> > Every FISON contains all its predecessors.
> Correct
> > The sequence of all FISONs contains all FISONs including all successors of all FISONs.
> Correct
> > The sequence of all FISONs contains the union of all FISONs.
> False,

Then find acounterexample, that is a FISON that is not contained in a union of FISONs contained in the sequence. Fail.

> the union of all FISONs is N but the sequence does not contain N

If |ℕ| = ℵo the union of FISONs is not ℕ. The union of all FISONs is contained in the sequence of all FISONs as a FISON. But all FISONs are finite, i.e., less than ℵo.

Regards, WM

Eram semper recta schrieb am Freitag, 1. April 2022 um 06:57:16 UTC+2:
> On Thursday, 31 March 2022 at 20:15:03 UTC+3, WM wrote:

> > > > The formula is p/q. The number has got the name p/q.
> > > Rubbish. formula =/= number.
> > But both can and do carry the same name.
> If you mean they are synonyms, no - the dictionary does not state as much.
>
> Formula: a mathematical relationship or rule expressed in symbols.

Here by p/q or 1/3.
>
> Number: an arithmetical value, expressed by a word, symbol, or figure,

Here by p/q or 1/3.

Regards, WM

The imbecile clown WM drivels:

> Generators generate. That's an activity.

No, there are no single steps.

Operation is no activity in math, nor is creation an activity, but one
object follows another one without (single or repeated) activity:

"In mathematics, an operation is a function which takes zero or more
input values (called operands) to a well-defined output value. The number
of operands (also known as arguments) is the arity of the operation."

Generation is no activity in math:
"the term generator or generating set may refer to any of a number
of related concepts. The underlying concept in each case is that of
a smaller set of objects, together with a set of operations that can
be applied to it, that result in the creation of a larger collection
of objects, called the generated set."

(wikipedia)

They have told you those basics vor 30 years now, piss off, idiot.

On Thursday, 31 March 2022 at 17:58:26 UTC-3, konyberg wrote:
> torsdag 31. mars 2022 kl. 22:28:13 UTC+2 skrev horand....@gmail.com:
[...]
> > The standard way to use a random process is to generate digits, for instance from tossing a coin. With such a process you know that each iterate is contained in a small interval that gets cut in half at each iteration. By completeness of the real numbers, a limit exists.
> I can use two numbers generated at random, 0 and 1. A random number is 0.101001000100001...
> Adding a 0 between the 1. This doesn't look random, but it could be. What is the limit?

You seem to be arguing like WM here. In the first instance it is important that there is a limit. Remember the intermediate value theorem: Let f be a continuous function on a finite, closed interval [a, b], and let c be a number between max{f(x): x in [a,b]} and min{f(x): x in [a,b]}. Then there exists an x in [a,b] such that f(x) = c. It's the same thing here. You can prove existence of the limit, and by the completeness of the real numbers, the limit (because it is finite) is a real number. The end.

Eram semper recta schrieb am Freitag, 1. April 2022 um 07:10:06 UTC+2:

> Your arguments about Cantor are 100% sound.

It is relieving to know that mathematicians can understand this.

> The number is NOT the formula.

Correct. But both can have the same notation. Like Millers and millers.

Regards, WM

The imbecile clown WM drivels:

>> Formula: a mathematical relationship or rule expressed in symbols.
>
> Here by p/q or 1/3.

This is a term, idiot.

"A term denotes a mathematical object while
a formula denotes a mathematical fact."

" In mathematics, a formula generally refers to an identity
w h i c h e q u a t e s

one mathematical expression to another, with the most important
ones being mathematical theorems. " (wiki)

Piss off, disgusting asshole.

On Thursday, 31 March 2022 at 18:02:26 UTC-3, WM wrote:
> William schrieb am Donnerstag, 31. März 2022 um 20:50:12 UTC+2:
> > On Thursday, March 31, 2022 at 3:01:50 PM UTC-3, WM wrote:
>
> > > To uphold this wrong assumption you must believe that the union over all FISONs contains more than all FISONs.
> > Nope you must believe that the union over all FISONs contains more than *any single FISON*.
> But it does not. In fact you must fix a FISON and then you can prove that the union is larger, Small wonder. But I do not fix a FISON but consider all of them. Each one is the union of all its predecessors. Therefore the union over all FISONs which can be unioned at all has already been done and is already in the sequence.
> {1} = {1}
> {1} U {1, 2} = {1, 2}
> {1} U {1, 2} U {1, 2, 3} = {1, 2, 3}
> {1} U {1, 2} U {1, 2, 3} U {1, 2, 3, 4} = {1, 2, 3, 4}
> {1} U {1, 2} U {1, 2, 3} U {1, 2, 3, 4} U {1, 2, 3, 4, 5} = {1, 2, 3, 4, 5}
> ...
> > This is equivalent to believing that there is no largest FISON.
> There is no largest FISON, but there is no ℵo-FISON. Hence the union over FISONs is not an ℵo-set.

Doesn't follow. There is no largest integer, but their number is still ℵo. No contradiction, your quantifier shifting below notwithstanding.
> You trick is too simple: Choose a FISON and show that it is not the union of all FISONs. I do not choose a FISON but use all available FISONs. But they are all finite. And the are all unions of all predecessors. Nothing more is available for the union. A union of ℵo different FISONs would require FISONs with more than any finite number of symbols:
>
> o
> oo
> ooo
> ...
>
> But so many are not available.

Why not? You are even doing it with a single symbol. In any finite alphabet there are ℵo finite strings.

The disgusting, imbecile Clown WM drivels:

> Eram semper recta schrieb am Freitag, 1. April 2022 um 07:10:06 UTC+2:
>
>> Your arguments about Cantor are 100% sound.
>
> It is relieving to know that mathematicians can understand this.
>
>> The number is NOT the formula.
>
> Correct. But both can have the same notation. Like Millers and millers.

Wrong, since formulas e q u a t e mathematical objects.

Piss off, asshole.

On Friday, 1 April 2022 at 06:44:42 UTC-3, WM wrote:
> Alan Mackenzie schrieb am Donnerstag, 31. März 2022 um 22:26:24 UTC+2:
[...]
> > So, why shouldn't
> > 0.570039362554378... also converge to a limit?
> If it does, the limit is unknown (dark) and unknowable: remaining dark forever.

That makes no difference. Existence proofs do not have to entail an algorithm for finding a solution. Think of the intermediate value theorem, if you can still remember it. (I would assume that you put that into your alleged textbook.)

On Friday, April 1, 2022 at 6:34:00 AM UTC-3, WM wrote:
> William schrieb am Donnerstag, 31. März 2022 um 20:40:18 UTC+2:
> > On Thursday, March 31, 2022 at 2:24:11 PM UTC-3, WM wrote:
>
> No single element *that you can define* contains the union.

Every element of the sequence can be defined.

"potential infinity of the sequence."

Absolute nonsense.

>
> But fact is that every union is contained in the sequence.

Nope. Any union of a subsequence with last element is not in the sequence.

--
William Hughes

horand....@gmail.com schrieb am Freitag, 1. April 2022 um 12:37:06 UTC+2:
> On Thursday, 31 March 2022 at 18:02:26 UTC-3, WM wrote:
> > William schrieb am Donnerstag, 31. März 2022 um 20:50:12 UTC+2:
> > > On Thursday, March 31, 2022 at 3:01:50 PM UTC-3, WM wrote:
> >
> > > > To uphold this wrong assumption you must believe that the union over all FISONs contains more than all FISONs.
> > > Nope you must believe that the union over all FISONs contains more than *any single FISON*.
> > But it does not. In fact you must fix a FISON and then you can prove that the union is larger, Small wonder. But I do not fix a FISON but consider all of them. Each one is the union of all its predecessors. Therefore the union over all FISONs which can be unioned at all has already been done and is already in the sequence.
> > {1} = {1}
> > {1} U {1, 2} = {1, 2}
> > {1} U {1, 2} U {1, 2, 3} = {1, 2, 3}
> > {1} U {1, 2} U {1, 2, 3} U {1, 2, 3, 4} = {1, 2, 3, 4}
> > {1} U {1, 2} U {1, 2, 3} U {1, 2, 3, 4} U {1, 2, 3, 4, 5} = {1, 2, 3, 4, 5}
> > ...
> > > This is equivalent to believing that there is no largest FISON.
> > There is no largest FISON, but there is no ℵo-FISON. Hence the union over FISONs is not an ℵo-set.
> Doesn't follow. There is no largest integer, but their number is still ℵo. No contradiction, your quantifier shifting below notwithstanding.
> > You trick is too simple: Choose a FISON and show that it is not the union of all FISONs. I do not choose a FISON but use all available FISONs. But they are all finite. And the are all unions of all predecessors. Nothing more is available for the union. A union of ℵo different FISONs would require FISONs with more than any finite number of symbols:
> >
> > o
> > oo
> > ooo
> > ...
> >
> > But so many are not available.
> Why not?

Pigeonhole principle. Denied by matheologians but nevertheless true for all finite sets. And FISONs are finite sets, no matter how many of them are concerned.

> You are even doing it with a single symbol.

That does not make a difference since in FISONs the numbers cannot change places.
1, 2, 3, 4, 5 expresses the same as ooooo. Therefore any finite set of n FISONs has at least one FISON with n symbols. This holds for all finite n. If there should be more than any finite number of FISONs then there must be a FISON with more than a finite number of symbols.

That is not a problem for matheologians however, because here they hasten to switch to potential infinity. A potentially infinite collection of FISONs needs no actually infinite FISON.

> In any finite alphabet there are ℵo finite strings.

No. That is only possibleif potential infinity, i.e., never reaching a number larger than every natnumber is denoted as ℵo, a number larger than every natnumber.

Regards, WM

On Friday, April 1, 2022 at 6:51:47 AM UTC-3, WM wrote:
> William schrieb am Donnerstag, 31. März 2022 um 23:45:33 UTC+2:
> > the resulting union is not one term of the sequence.
> That is matheology. What term

Not a term but a subset (any subset without last element)

--
William Hughes

William schrieb am Freitag, 1. April 2022 um 13:26:43 UTC+2:
> On Friday, April 1, 2022 at 6:34:00 AM UTC-3, WM wrote:
> > William schrieb am Donnerstag, 31. März 2022 um 20:40:18 UTC+2:
> > > On Thursday, March 31, 2022 at 2:24:11 PM UTC-3, WM wrote:
> >
> > No single element *that you can define* contains the union.
> Every element of the sequence can be defined.
> "potential infinity of the sequence."
> Absolute nonsense.

Unavoidable truth.
> >
> > But fact is that every union is contained in the sequence.
> Nope. Any union of a subsequence with last element is not in the sequence..

The potentially infinite sequence contains all FISONs and all unions of FISONs. Nothing remains to make the last union larger. Or could you find something, i.e., a FISON not unioned in a term of the sequence?

Regards, WM

The disgusting, imbecile Clown WM drivels:

> potential infinity

Nonsense, piss off, idiot.