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ralfkannenberg
Anmeldedatum: 22.02.2006
Beiträge: 4788
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 Verfasst am: 20.12.2009, 22:55 Titel: |
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| JANm hat Folgendes geschrieben: | Kenne nur zwei die ich bezweifle.
1 Unzahlbarkeit von reale zahlen
(...)
Zum ersten glaub ich das es moglich sei zahlbarkeit zu erreichen. |
Hallo Jan,
wenn Du den Unterschied kennst zwischen:
- "für alle gilt" und
- "es gibt mindestens einen, für den gilt",
dann kannst Du die Abzählbarkeit für das Kontinuum nicht erreichen.
Somit empfehle ich also, einen allfälligen Beweis pedantisch genau auf die Definition der Gleichmächtigkeit und o.g. Unterschied zu überprüfen.
| JANm hat Folgendes geschrieben: | | Ich habe immer mathematic studiert (...) |
Hast Du auch einen Abschluss ? 
Freundliche Grüsse, Ralf |
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JANm
Anmeldedatum: 08.10.2008
Beiträge: 322
Wohnort: Haarlem, Nederland
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| Verfasst am: 21.12.2009, 00:06 Titel: |
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[quote="ralfkannenberg"] | JANm hat Folgendes geschrieben: | kennst zwischen:
- "für alle gilt" und
- "es gibt mindestens einen, für den gilt",
dann kannst Du die Abzählbarkeit für das Kontinuum nicht erreichen.
Somit empfehle ich also, einen allfälligen Beweis pedantisch genau auf die Definition der Gleichmächtigkeit und o.g. Unterschied zu überprüfen.
| JANm hat Folgendes geschrieben: | | Ich habe immer mathematic studiert (...) |
Hast Du auch einen Abschluss ? ;) |
Hallo Ralf
Zum Zweiten: du hast recht Ralf ich wolte sagen das nur gans genau erinnern von ein beweis nicht ganz mein sache war und das dass ist was getestet wird. Ein monat spater mag es vergessen sein copiiermachine zum beweisen ist was mathematic heist?
Zum ersten
Das ganze raum ist gleichmachtig mit ein kugel mit einhalt, mit ein flach mit ein linien und mit ein linienstrecke schwischen 0 und 1. Sorry hab diesen Cantor sprung gemacht ohne es zu sagen.
Ich nehme es binair, also 0,(1)repetent=1.
Das beweis geht: nehme an Zahlen n auf die strecke 0<= n < 1 sind zahlbar sage n_i dann ist es moglich ein zahl zu construieren der nicht in die reihe forkomt...
Repetentie ist dort gans nicht genennt. Mein contrabeweis fur diese stellung ist das fur jede solche construction ist es moglich ein abzahlung zu machen wobei diese construierte zahl wohl vorkomt.
Mit das alle wolte ich nicht sagen das die stellung nicht richtig ist aber nachdem: 1 ist es gerechtigt zu glauben das er nicht richtig ist weil das beweis nicht stimmt
2 Wan man kritik zu so einem sache nicht anhort ist mathematic un undemocratische glauberei wobei man das ganze beweisen hinterwege lassen kan. Dan gibt es nie erneuerung oder verbesserung, kein klarheit...
grusse Janm
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ralfkannenberg
Anmeldedatum: 22.02.2006
Beiträge: 4788
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| Verfasst am: 21.12.2009, 00:10 Titel: |
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| JANm hat Folgendes geschrieben: | Zum ersten
(...) |
Hallo JANm,
könntest Du das bitte auf englisch führen ? Dieser Sprachen-Mix führt bei mathematischen Erörterungen leider zu Missverständnissen.
Freundliche Grüsse, Ralf |
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JANm
Anmeldedatum: 08.10.2008
Beiträge: 322
Wohnort: Haarlem, Nederland
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| Verfasst am: 21.12.2009, 12:12 Titel: |
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Hello Ralf
In the first place I forgot to mention that checking proofs while studying is a much harder way then just remembering it. Of course in this way it is remembered the best. From the hundreds of proofs I "read" in this way two still remain questioned. The one of finding a way in the labirinth and the other is supracountibility of R or as you rightly say a piece of R between 0 and 1.
Since 0,1111111=1 for the binary numbers while it is the simplest geometric sum which prooves that Achilles never reaches the turtle, decimal representation is not an unique way of describing numbers.
0,101=5/8=0,10011111111111111111etcetera,
0,(101repetent)=5/8+5/64+5/512=5/8/(1-1/8)=5/7 can thus be written in many ways.
Construction of a number which is not in a row n_i by changing the binary in: 0,1=1/2; 0,(01rep)=1/3; 0,(10rep)=2/3;0,01=1/4; 0,11=3/4;etc gives: 0,00011
but it can always be sicumsized by putting in one of the other ways of describing the numbers. For instance if u use 0,0011111111=1/4 then the constructed number will be: 0,00001
This indistinction makes this proof flaud.
QED Janm.
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ralfkannenberg
Anmeldedatum: 22.02.2006
Beiträge: 4788
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| Verfasst am: 21.12.2009, 13:41 Titel: |
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| JANm hat Folgendes geschrieben: | | Hello Ralf |
Hi JANm,
thank you for answering in Engish to avoid misunerstandings.
| JANm hat Folgendes geschrieben: | | Since 0,1111111=1 for the binary numbers while it is the simplest geometric sum which prooves that Achilles never reaches the turtle, decimal representation is not an unique way of describing numbers. |
(1) this does not prove that Achilles never reaches the turtle as this representation is not equidistant in time, i.e. nowhere is written how much time passes between 2 summands. In fact the time intervalls also converge to 0 as the distance between Achilles and the turtle does. Thus such situations require a more thoroughful investigation.
In this special situation the solution is easy as the whole situation converges to the meeting point of Achilles and the turtle.
(2) decimal representations of numbers can be ambiguous as e.g. for binary representations 0.1111... = 1.0.
You can easily prove this equation by taking any epsilon > 0; now you can find a delta where the difference of 1-0.1111... < epsilon. As you can do this for all epsilon > 0 (including the very small ones !!), i.e. for all epsilon > 0 you find such a delta. Now you look how convergement is defined and you see immediatey that the equation above is proved.
In the decimal system the ambigiousness is 1 = 0.9999999.....
| JANm hat Folgendes geschrieben: | Construction of a number which is not in a row n_i by changing the binary in: 0,1=1/2; 0,(01rep)=1/3; 0,(10rep)=2/3;0,01=1/4; 0,11=3/4;etc gives: 0,00011
but it can always be sicumsized by putting in one of the other ways of describing the numbers. For instance if u use 0,0011111111=1/4 then the constructed number will be: 0,00001
This indistinction makes this proof flaud.
QED |
Can you please tell me what exactly you want to prove with this statement ? - If you "discover" that decimal representations of numbers are not unique you just have to make a convention which representation you want to use and exclude the other one as you do not want to map representations but the numbers themselves.
Cheers, Ralf |
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JANm
Anmeldedatum: 08.10.2008
Beiträge: 322
Wohnort: Haarlem, Nederland
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| Verfasst am: 21.12.2009, 14:12 Titel: |
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[quote="ralfkannenberg"] | JANm hat Folgendes geschrieben: | Can you please tell me what exactly you want to prove with this statement ?
Cheers, Ralf |
Hello Ralf
What I want to prove is that things in mathematics are
"beyond all doubt"
if people listen to kritic. While a proof is doubted the possibility exists that the these is wrong. This is how it works in mathematics. There must be something similar for physics. The path of experiments to ensure difference between theories...
greetings Janm
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ralfkannenberg
Anmeldedatum: 22.02.2006
Beiträge: 4788
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| Verfasst am: 22.12.2009, 13:34 Titel: |
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| JANm hat Folgendes geschrieben: | What I want to prove is that things in mathematics are
"beyond all doubt"
if people listen to kritic. While a proof is doubted the possibility exists that the these is wrong. This is how it works in mathematics. There must be something similar for physics. |
Hi JANm,
of course there is. Physical theories are questioned all the time. But they can only be questioned by people who have understood both theses !
Just to avoid misunderstandings: Do you now accept the correctness of Cantor's proof, that there cannot be a bijection between IN and [0,1] ?
Cheers, Ralf |
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JANm
Anmeldedatum: 08.10.2008
Beiträge: 322
Wohnort: Haarlem, Nederland
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| Verfasst am: 22.12.2009, 14:11 Titel: |
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| ralfkannenberg hat Folgendes geschrieben: |
of course there is. Physical theories are questioned all the time. But they can only be questioned by people who have understood both theses !
Just to avoid misunderstandings: Do you now accept the correctness of Cantor's proof, that there cannot be a bijection between IN and [0,1] ?
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Hello Ralf
About the first: sometimes there is only one these and the thing I see there is that experiments in this case are used to confirm something of which one already seems to be sure of. Is it then rightful to speak of an experiment?
About the second: I don't know it is the proof of Cantor about supracountibility. By my knowledge Cantor prooved the "gleichmachtigkeit" of Descartian space, a flat surface, a line and a part of a line. It seems that this conclusion overwhelmed him...
Since the complex numbers plus or minus one point is "gleichmachtig" with the real numbers and this with a line piece it suffices to count the number of points between 0 and 1. That is what Cantor prooved and is correct. The these I put in discussion is are the number points between 0 and 1 are larger then countable. As a antithese I pose that they could be countable because I state that the proof which is commonly used has a flaud...
greetings Janm
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JANm
Anmeldedatum: 08.10.2008
Beiträge: 322
Wohnort: Haarlem, Nederland
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| Verfasst am: 22.12.2009, 20:12 Titel: Instrument Analysis |
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| ralfkannenberg hat Folgendes geschrieben: | [
of course there is. Physical theories are questioned all the time. But they can only be questioned by people who have understood both theses !
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Hello Ralf
I continued with this because that is what this thread is most about.
There are three things to be considered
1 Instruments New, Tested or Faulty
2 Objects Known or Unknown
3 Measurements Positive or Zero
If it is possible that a new instrument can be tested with a known object then it becomes tested, or faulty. The experiment there is testing the instrument.
A positive measurement of an unknown object makes a new instrument tested. The experiment there was to find (and measure) something new.
A tested instrument can deduce objects by measurements. The word experiment is here too big it is just measuring.
For the combination of Instrument=New, Objects=unknown and Measurement=0
the question arises what is the experiment there and what conclusions can be drawn of such a case...
Hope to have been of service,
cheers Janm
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ralfkannenberg
Anmeldedatum: 22.02.2006
Beiträge: 4788
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| Verfasst am: 23.12.2009, 13:21 Titel: |
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| JANm hat Folgendes geschrieben: | | About the second: I don't know it is the proof of Cantor about supracountibility. By my knowledge Cantor prooved the "gleichmachtigkeit" of Descartian space, a flat surface, a line and a part of a line. It seems that this conclusion overwhelmed him... |
Hi JANm,
I just recommend you to read the proof before you talk about it ........
| JANm hat Folgendes geschrieben: | | Since the complex numbers plus or minus one point |
Could you please define what "complex numbers plus or minus one point" are supposed to be according to your opinion ?
| JANm hat Folgendes geschrieben: | | (...) is "gleichmachtig" with the real numbers and this with a line piece it suffices to count the number of points between 0 and 1. That is what Cantor prooved and is correct. |
No. This is trivial and not the issue of Cantor's proof.
Cheers, Ralf |
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JANm
Anmeldedatum: 08.10.2008
Beiträge: 322
Wohnort: Haarlem, Nederland
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| Verfasst am: 24.12.2009, 20:56 Titel: |
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| ralfkannenberg hat Folgendes geschrieben: | | [Could you please define what "complex numbers plus or minus one point" are supposed to be according to your opinion ? |
Hello Ralf
In the day scientists had to fight against the opinion that the earth was flat and artist were busy trying to understand projection; nowadays known in mathematics as well as psychology one invented the projective plane. Since it is not my strongest part of mathematical attendance I said plus or minus one point. In projectivity is believed that lines and circles must have similar properties: A line is a circle with an endless radius and a circle connects the "beginning" of the line with the "end". If you make a point projection of a plane V , by giving a point P not in the plane and the plane itself then every point Q in the plane corresponds to a line(P,Q) to define a point for every line through P an extra point was needed for the paralel lines to V and only one because going into infinity on plane V one gets a paralel line to V.
Conclusion All lines through a point P can be associated with a plane plus one point.
Think that was the projectivity thing...
Greetings Janm
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ralfkannenberg
Anmeldedatum: 22.02.2006
Beiträge: 4788
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| Verfasst am: 27.12.2009, 21:34 Titel: |
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| JANm hat Folgendes geschrieben: | | In projectivity is believed that lines and circles must have similar properties: |
Hi JANm,
ok, maybe - I have not checked these arguments of you thoroughly now as they do not seem to be the main focus in our current discussion. Anyway my question: Where is the relation to Cantor's proof ?
I assume that you are aware that the difference of a finite number of points does not change anything regarding "Abzählbarkeit".
Best regards, Ralf |
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JANm
Anmeldedatum: 08.10.2008
Beiträge: 322
Wohnort: Haarlem, Nederland
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| Verfasst am: 28.12.2009, 00:05 Titel: 3rd Xmas Day, near the end. |
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| ralfkannenberg hat Folgendes geschrieben: | [I assume that you are aware that the difference of a finite number of points does not change anything regarding "Abzählbarkeit".
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Hello Ralf
Indeed the infinity of a finite number of points (rememberences of occurences in fourdimensional space, perhaps a little enlenghtened in time; Inches or meters as a Lenghtparameter does not matter at that moment being satisfied that luckily everybody on earth is contented with seconds, minutes, hours, days, yaers, centuries and milenia (a thing perhaps also to reconsider in adjusting to decimality)) is countable, perhaps that is for the best. Technically everybody also has his/her emotions and if those are not finite on a third Xmas or even a total lifetime that is called: TOO MUCH.
Afterwords spoken,
nice Chrismas Ralf and all, Janm
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